64:@0.058194:0.966765:0.075166:0.966765:0.075166:0.950778:0.058194:0.950778:0.000000:0.000000
Competencia :@0.199646:0.414841:0.297269:0.414841:0.297269:0.399368:0.199646:0.399368:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
comunicacional:@0.199646:0.427409:0.311604:0.427409:0.311604:0.411936:0.199646:0.411936:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Aprende las siguientes :@0.193074:0.451883:0.341127:0.451883:0.341127:0.436820:0.193074:0.436820:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
definiciones::@0.153338:0.467725:0.234407:0.467725:0.234407:0.452662:0.153338:0.452662:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean  ,   dos funciones  :@0.153338:0.490696:0.312825:0.490696:0.312825:0.475633:0.153338:0.475633:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p q:@0.187850:0.490802:0.210981:0.490802:0.210981:0.475765:0.187850:0.475765:0.000000:0.000000:0.000000
polinomiales.:@0.153338:0.506538:0.239332:0.506538:0.239332:0.491475:0.153338:0.491475:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La función real  , definida como:@0.153338:0.529509:0.357680:0.529509:0.357680:0.514446:0.153338:0.514446:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.252546:0.529615:0.256468:0.529615:0.256468:0.514578:0.252546:0.514578:0.000000
f:@0.153338:0.555332:0.157261:0.555332:0.157261:0.540295:0.153338:0.540295:0.000000
 =   ,     ≠ 0,:@0.157261:0.555226:0.242658:0.555220:0.242658:0.540157:0.157261:0.540163:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.177593:0.548421:0.186054:0.548421:0.186054:0.533385:0.177593:0.533385:0.000000
q:@0.177628:0.566019:0.186001:0.566019:0.186001:0.550983:0.177628:0.550983:0.000000
q:@0.206581:0.555326:0.214954:0.555326:0.214954:0.540289:0.206581:0.540289:0.000000
se llama :@0.153336:0.583881:0.208903:0.583881:0.208903:0.568818:0.153336:0.568818:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función racional:@0.208903:0.584079:0.318575:0.584079:0.318575:0.568818:0.208903:0.568818:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.318577:0.583881:0.321092:0.583881:0.321092:0.568818:0.318577:0.568818:0.000000
Nota que la función polinomial :@0.153336:0.599723:0.361124:0.599723:0.361124:0.584660:0.153336:0.584660:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
q:@0.153336:0.615671:0.161709:0.615671:0.161709:0.600634:0.153336:0.600634:0.000000
 no es nula.:@0.161709:0.615565:0.234813:0.615565:0.234813:0.600502:0.161709:0.600502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La función real  , definida:@0.153336:0.638536:0.315743:0.638536:0.315743:0.623473:0.153336:0.623473:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.252544:0.638642:0.256467:0.638642:0.256467:0.623605:0.252544:0.623605:0.000000
como   =   = 0, se llama :@0.153336:0.664253:0.317940:0.664259:0.317940:0.649195:0.153336:0.649190:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.195271:0.664358:0.199194:0.664358:0.199194:0.649322:0.195271:0.649322:0.000000
p:@0.219526:0.657460:0.227987:0.657460:0.227987:0.642423:0.219526:0.642423:0.000000
q:@0.219579:0.675057:0.227952:0.675057:0.227952:0.660021:0.219579:0.660021:0.000000
función racional nula:@0.153352:0.687084:0.296308:0.687084:0.296308:0.671823:0.153352:0.671823:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.296306:0.687309:0.299983:0.687309:0.299983:0.671836:0.296306:0.671836:0.000000
y se :@0.299983:0.686886:0.327986:0.686886:0.327986:0.671823:0.299983:0.671823:0.000000:0.000000:0.000000:0.000000:0.000000
representa simplemente con 0, :@0.153352:0.702728:0.356390:0.702728:0.356390:0.687665:0.153352:0.687665:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
siempre que no haya peligro de :@0.153352:0.718570:0.360102:0.718570:0.360102:0.703507:0.153352:0.703507:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
confusión.:@0.153352:0.734412:0.220210:0.734412:0.220210:0.719349:0.153352:0.719349:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Recordemos que si  ,      ,  :@0.153352:0.758888:0.348291:0.758900:0.348291:0.743837:0.153352:0.743825:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.279875:0.758994:0.302830:0.758994:0.302830:0.743957:0.279875:0.743957:0.000000:0.000000:0.000000
:@0.306612:0.758690:0.321265:0.758690:0.321265:0.745317:0.306612:0.745317:0.000000
:@0.324687:0.758252:0.338597:0.758252:0.338597:0.744805:0.324687:0.744805:0.000000
a:@0.156371:0.774250:0.164568:0.774250:0.164568:0.759214:0.156371:0.759214:0.000000
b:@0.156230:0.791848:0.164691:0.791848:0.164691:0.776811:0.156230:0.776811:0.000000
     :@0.167576:0.781049:0.206761:0.781055:0.206761:0.765992:0.167576:0.765986:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.171358:0.780851:0.186010:0.780851:0.186010:0.767478:0.171358:0.767478:0.000000
:@0.189455:0.780407:0.203365:0.780407:0.203365:0.766960:0.189455:0.766960:0.000000
⇔:@0.206762:0.780455:0.224218:0.780455:0.224218:0.765053:0.206762:0.765053:0.000000
 :@0.224168:0.780593:0.228566:0.780593:0.228566:0.764421:0.224168:0.764421:0.000000
b:@0.228513:0.781160:0.236974:0.781160:0.236974:0.766124:0.228513:0.766124:0.000000
 ≠ 0. Esto es,   :@0.236974:0.781055:0.337550:0.781049:0.337550:0.765986:0.236974:0.765992:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.322563:0.774250:0.330760:0.774250:0.330760:0.759214:0.322563:0.759214:0.000000
b:@0.322422:0.791848:0.330883:0.791848:0.330883:0.776811:0.322422:0.776811:0.000000
está bien definido si y solo si el :@0.153330:0.805697:0.355562:0.805697:0.355562:0.790634:0.153330:0.790634:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
denominador   ≠ 0.:@0.153330:0.821539:0.282931:0.821539:0.282931:0.806476:0.153330:0.806476:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.246766:0.821644:0.255227:0.821644:0.255227:0.806608:0.246766:0.806608:0.000000
Operaciones con funciones racionales:@0.404235:0.116974:0.857152:0.116974:0.857152:0.072315:0.404235:0.072315:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.45. Realizar operaciones de suma y multiplicación entre funciones racionales y de multiplicación de números reales por funciones racionales en ejercicios algebraicos, :@0.144321:0.942136:0.894370:0.942136:0.894370:0.932094:0.144321:0.932094:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para simplificar las funciones. :@0.144321:0.950937:0.272925:0.950937:0.272925:0.940895:0.144321:0.940895:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Adición de funciones racionales:@0.404236:0.138314:0.658733:0.138314:0.658733:0.120632:0.404236:0.120632:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean :@0.404236:0.155022:0.442035:0.155022:0.442035:0.138524:0.404236:0.138524:0.000000:0.000000:0.000000:0.000000:0.000000
p, q, r, s:@0.441630:0.155138:0.490333:0.155138:0.490333:0.138669:0.441630:0.138669:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 polinomios reales de grado ≤ 2,   y   dos funciones racio-:@0.490333:0.155022:0.891782:0.155022:0.891782:0.138524:0.490333:0.138524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f g:@0.718183:0.155138:0.745212:0.155138:0.745212:0.138669:0.718183:0.138669:0.000000:0.000000:0.000000
nales definidas como::@0.404255:0.172373:0.557104:0.172373:0.557104:0.155875:0.404255:0.155875:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.404255:0.196968:0.421594:0.196968:0.421594:0.180499:0.404255:0.180499:0.000000:0.000000:0.000000
( ) =          ,        :@0.408359:0.196852:0.542439:0.196851:0.542439:0.180354:0.408359:0.180354:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∀:@0.499752:0.204438:0.511324:0.204438:0.511324:0.185439:0.499752:0.185439:0.000000
x:@0.511331:0.196967:0.518806:0.196967:0.518806:0.180498:0.511331:0.180498:0.000000
:@0.522947:0.196483:0.538297:0.196483:0.538297:0.182473:0.522947:0.182473:0.000000
Dom f:@0.542247:0.196967:0.586942:0.196967:0.586942:0.180498:0.542247:0.180498:0.000000:0.000000:0.000000:0.000000:0.000000
( ),     ( ) =           ,        :@0.576886:0.196851:0.756932:0.196851:0.756932:0.180354:0.576886:0.180354:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g x:@0.611640:0.196967:0.632119:0.196967:0.632119:0.180498:0.611640:0.180498:0.000000:0.000000:0.000000
∀:@0.714243:0.204438:0.725815:0.204438:0.725815:0.185439:0.714243:0.185439:0.000000
x:@0.725824:0.196967:0.733298:0.196967:0.733298:0.180498:0.725824:0.180498:0.000000
:@0.737440:0.196483:0.752790:0.196483:0.752790:0.182473:0.737440:0.182473:0.000000
Dom g:@0.756739:0.196967:0.804575:0.196967:0.804575:0.180498:0.756739:0.180498:0.000000:0.000000:0.000000:0.000000:0.000000
( ).:@0.791378:0.196851:0.812898:0.196851:0.812898:0.180354:0.791378:0.180354:0.000000:0.000000:0.000000:0.000000
Definición:@0.404243:0.240315:0.484327:0.240315:0.484327:0.223369:0.404243:0.223369:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Se define la función   +   como sigue::@0.484329:0.239852:0.754961:0.239852:0.754961:0.223354:0.484329:0.223354:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f g:@0.635461:0.239968:0.666285:0.239968:0.666285:0.223499:0.635461:0.223499:0.000000:0.000000:0.000000
( +  )( ) =  ( ) +  ( ) =                                  ,     :@0.404243:0.267888:0.760383:0.267894:0.760383:0.251396:0.404243:0.251390:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f  g x:@0.410196:0.268004:0.460401:0.268004:0.460401:0.251535:0.410196:0.251535:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.485446:0.268004:0.503170:0.268004:0.503170:0.251535:0.485446:0.251535:0.000000:0.000000:0.000000
g x:@0.528215:0.268004:0.549079:0.268004:0.549079:0.251535:0.528215:0.251535:0.000000:0.000000:0.000000
∀:@0.717694:0.275480:0.729266:0.275480:0.729266:0.256481:0.717694:0.256481:0.000000
x:@0.729275:0.268009:0.736749:0.268009:0.736749:0.251541:0.729275:0.251541:0.000000
:@0.740891:0.267526:0.756241:0.267526:0.756241:0.253516:0.740891:0.253516:0.000000
Dom f:@0.760190:0.268009:0.804886:0.268009:0.804886:0.251541:0.760190:0.251541:0.000000:0.000000:0.000000:0.000000:0.000000
( )   :@0.794829:0.267894:0.834593:0.267894:0.834593:0.251396:0.794829:0.251396:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.814403:0.267677:0.830451:0.267677:0.830451:0.253030:0.814403:0.253030:0.000000
Dom g:@0.834400:0.268009:0.882236:0.268009:0.882236:0.251541:0.834400:0.251541:0.000000:0.000000:0.000000:0.000000:0.000000
( ).:@0.869039:0.267894:0.890558:0.267894:0.890558:0.251396:0.869039:0.251396:0.000000:0.000000:0.000000:0.000000
En forma abreviada escribimos:  +   =      +      =               ,   ≠ 0,   ≠ 0.:@0.404245:0.320409:0.889225:0.320409:0.889225:0.303911:0.404245:0.303911:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f  g:@0.628508:0.320524:0.659333:0.320524:0.659333:0.304056:0.628508:0.304056:0.000000:0.000000:0.000000:0.000000
q:@0.808850:0.320524:0.818021:0.320524:0.818021:0.304056:0.808850:0.304056:0.000000
s:@0.852506:0.320524:0.858882:0.320524:0.858882:0.304056:0.852506:0.304056:0.000000
Las imágenes de funciones racionales son números reales, por lo tan-:@0.404245:0.362238:0.891809:0.362238:0.891809:0.345741:0.404245:0.345741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
to, las operaciones con funciones racionales heredan las propiedades :@0.404245:0.379589:0.895983:0.379589:0.895983:0.363092:0.404245:0.363092:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
algebraicas de los números reales. :@0.404245:0.396940:0.645233:0.396940:0.645233:0.380442:0.404245:0.380442:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dadas las funciones racionales  ,  , la función   +   está definida única-:@0.404245:0.431641:0.891751:0.431641:0.891751:0.415144:0.404245:0.415144:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f g:@0.621226:0.431757:0.639397:0.431757:0.639397:0.415288:0.621226:0.415288:0.000000:0.000000:0.000000
f g:@0.719828:0.431757:0.749727:0.431757:0.749727:0.415288:0.719828:0.415288:0.000000:0.000000:0.000000
mente en el conjunto  :@0.404245:0.448992:0.565919:0.448992:0.565919:0.432495:0.404245:0.432495:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dom f:@0.565919:0.449108:0.611385:0.449108:0.611385:0.432639:0.565919:0.432639:0.000000:0.000000:0.000000:0.000000:0.000000
( )   :@0.601136:0.448992:0.640960:0.448999:0.640960:0.432501:0.601136:0.432495:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.621470:0.448631:0.636820:0.448631:0.636820:0.434621:0.621470:0.434621:0.000000
Dom g:@0.640960:0.449115:0.689566:0.449115:0.689566:0.432646:0.640960:0.432646:0.000000:0.000000:0.000000:0.000000:0.000000
( ).:@0.676177:0.448999:0.698274:0.448999:0.698274:0.432501:0.676177:0.432501:0.000000:0.000000:0.000000:0.000000
Ejercicio resuelto:@0.404229:0.484077:0.522207:0.484077:0.522207:0.467290:0.404229:0.467290:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Consideremos las funciones racionales  ,  , definidas como sigue::@0.404229:0.501051:0.859266:0.501051:0.859266:0.484554:0.404229:0.484554:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f g:@0.680643:0.501167:0.699272:0.501167:0.699272:0.484698:0.680643:0.484698:0.000000:0.000000:0.000000
 :@0.427979:0.529062:0.432085:0.529062:0.432085:0.512708:0.427979:0.512708:0.000000
f x:@0.451718:0.529177:0.469288:0.529177:0.469288:0.512851:0.451718:0.512851:0.000000:0.000000:0.000000
( ) =           ,   :@0.455977:0.529062:0.551370:0.529062:0.551370:0.512708:0.455977:0.512708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∀:@0.551372:0.536681:0.562945:0.536681:0.562945:0.517682:0.551372:0.517682:0.000000
x:@0.562953:0.529210:0.570428:0.529210:0.570428:0.512741:0.562953:0.512741:0.000000
   :@0.570428:0.529094:0.594062:0.529094:0.594062:0.512597:0.570428:0.512597:0.000000:0.000000:0.000000
:@0.574570:0.528726:0.589920:0.528726:0.589920:0.514716:0.574570:0.514716:0.000000
:@0.593868:0.528007:0.607173:0.528007:0.607173:0.515145:0.593868:0.515145:0.000000
 \ {1},:@0.606804:0.529062:0.640989:0.529062:0.640989:0.512708:0.606804:0.512708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.427979:0.565729:0.432121:0.565729:0.432121:0.549232:0.427979:0.549232:0.000000
g x:@0.451714:0.565845:0.472578:0.565845:0.472578:0.549376:0.451714:0.549376:0.000000:0.000000:0.000000
( ) =             ,       :@0.459151:0.565729:0.605204:0.565729:0.605204:0.549232:0.459151:0.549232:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∀:@0.562515:0.573316:0.574087:0.573316:0.574087:0.554317:0.562515:0.554317:0.000000
x:@0.574095:0.565845:0.581570:0.565845:0.581570:0.549376:0.574095:0.549376:0.000000
:@0.585712:0.565362:0.601062:0.565362:0.601062:0.551352:0.585712:0.551352:0.000000
:@0.605012:0.564643:0.618317:0.564643:0.618317:0.551780:0.605012:0.551780:0.000000
 \ :@0.617947:0.565697:0.630895:0.565697:0.630895:0.549343:0.617947:0.549343:0.000000:0.000000:0.000000
{–1, 1}.:@0.630512:0.565729:0.676672:0.565729:0.676672:0.549232:0.630512:0.549232:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
De la definición de las funciones racionales  ,  , se tiene:  :@0.404242:0.603829:0.803491:0.603829:0.803491:0.587331:0.404242:0.587331:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f g:@0.712656:0.603945:0.731285:0.603945:0.731285:0.587476:0.712656:0.587476:0.000000:0.000000:0.000000
Dom f:@0.404242:0.621295:0.449708:0.621295:0.449708:0.604827:0.404242:0.604827:0.000000:0.000000:0.000000:0.000000:0.000000
( ) =   \ {1}, :@0.439459:0.621180:0.525923:0.621174:0.525923:0.604676:0.439459:0.604682:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.474745:0.620087:0.488050:0.620087:0.488050:0.607225:0.474745:0.607225:0.000000
Dom g:@0.525538:0.621290:0.574144:0.621290:0.574144:0.604821:0.525538:0.604821:0.000000:0.000000:0.000000:0.000000:0.000000
( ) =   \ {–1, 1}. Entonces,  +   es la función :@0.560755:0.621174:0.875645:0.621174:0.875645:0.604676:0.560755:0.604676:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.599185:0.620087:0.612490:0.620087:0.612490:0.607225:0.599185:0.607225:0.000000
f  g:@0.747244:0.621290:0.778069:0.621290:0.778069:0.604821:0.747244:0.604821:0.000000:0.000000:0.000000:0.000000
racional definida como::@0.404230:0.638525:0.571183:0.638525:0.571183:0.622027:0.404230:0.622027:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(  +  )( ) =  ( ) +  ( ) =           +:@0.404230:0.664782:0.626339:0.664782:0.626339:0.648285:0.404230:0.648285:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f g x:@0.410183:0.664898:0.460389:0.664898:0.460389:0.648429:0.410183:0.648429:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.485433:0.664898:0.503157:0.664898:0.503157:0.648429:0.485433:0.648429:0.000000:0.000000:0.000000
g x:@0.528202:0.664898:0.549067:0.664898:0.549067:0.648429:0.528202:0.648429:0.000000:0.000000:0.000000
 :@0.404230:0.701841:0.408372:0.701841:0.408372:0.685343:0.404230:0.685343:0.000000
=           +                           =:@0.470715:0.701841:0.659378:0.701841:0.659378:0.685343:0.470715:0.685343:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404230:0.742456:0.408372:0.742456:0.408372:0.725958:0.404230:0.725958:0.000000
=                              =                          =:@0.470715:0.742456:0.735092:0.742456:0.735092:0.725958:0.470715:0.725958:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404230:0.781292:0.408372:0.781292:0.408372:0.764795:0.404230:0.764795:0.000000
=               = 3 +           , :@0.470715:0.781292:0.632580:0.781292:0.632580:0.764795:0.470715:0.764795:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∀:@0.632580:0.789391:0.644678:0.789391:0.644678:0.769529:0.632580:0.769529:0.000000
x:@0.644678:0.781408:0.652153:0.781408:0.652153:0.764939:0.644678:0.764939:0.000000
   :@0.652153:0.781292:0.675797:0.781287:0.675797:0.764790:0.652153:0.764795:0.000000:0.000000:0.000000
:@0.656304:0.780920:0.671655:0.780920:0.671655:0.766910:0.656304:0.766910:0.000000
:@0.675605:0.780201:0.688910:0.780201:0.688910:0.767338:0.675605:0.767338:0.000000
 \ :@0.688539:0.781255:0.701488:0.781255:0.701488:0.764901:0.688539:0.764901:0.000000:0.000000:0.000000
{–1, 1}.:@0.701107:0.781287:0.747267:0.781287:0.747267:0.764790:0.701107:0.764790:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404236:0.802297:0.409099:0.802297:0.409099:0.782930:0.404236:0.782930:0.000000
 :@0.404236:0.819006:0.408378:0.819006:0.408378:0.802509:0.404236:0.802509:0.000000
Esta función tiene dos asíntotas: una horizontal definida :@0.427971:0.819006:0.830438:0.819006:0.830438:0.802509:0.427971:0.802509:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como   = {( , 3) |   :@0.427971:0.836357:0.575234:0.836357:0.575234:0.819860:0.427971:0.819860:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.473899:0.836473:0.485170:0.836473:0.485170:0.820004:0.473899:0.820004:0.000000
h:@0.485120:0.839701:0.490601:0.839701:0.490601:0.830100:0.485120:0.830100:0.000000
x:@0.521503:0.836473:0.528978:0.836473:0.528978:0.820004:0.521503:0.820004:0.000000
x:@0.563617:0.836473:0.571092:0.836473:0.571092:0.820004:0.563617:0.820004:0.000000
 :@0.575234:0.836140:0.596098:0.836140:0.596098:0.821493:0.575234:0.821493:0.000000:0.000000
:@0.596095:0.835270:0.609399:0.835270:0.609399:0.822408:0.596095:0.822408:0.000000
} y una vertical dada como :@0.609399:0.836357:0.803358:0.836357:0.803358:0.819860:0.609399:0.819860:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.427979:0.853824:0.439249:0.853824:0.439249:0.837355:0.427979:0.837355:0.000000
v:@0.438749:0.857052:0.443287:0.857052:0.443287:0.847451:0.438749:0.847451:0.000000
 = {(–1,  ) |   :@0.443286:0.853708:0.538842:0.853708:0.538842:0.837210:0.443286:0.837210:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y y:@0.500080:0.853824:0.534700:0.853824:0.534700:0.837355:0.500080:0.837355:0.000000:0.000000:0.000000
 :@0.538842:0.853491:0.559706:0.853491:0.559706:0.838844:0.538842:0.838844:0.000000:0.000000
:@0.559703:0.852621:0.573008:0.852621:0.573008:0.839759:0.559703:0.839759:0.000000
}.:@0.573008:0.853708:0.581620:0.853708:0.581620:0.837210:0.573008:0.837210:0.000000:0.000000
 :@0.404245:0.886906:0.408387:0.886906:0.408387:0.870408:0.404245:0.870408:0.000000
Es preciso recalcar que en el cálculo de (  +  )( ) hemos utilizado :@0.427979:0.886906:0.895944:0.886906:0.895944:0.870408:0.427979:0.870408:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.715953:0.887021:0.720249:0.887021:0.720249:0.870553:0.715953:0.870553:0.000000
g x:@0.740188:0.887021:0.767005:0.887021:0.767005:0.870553:0.740188:0.870553:0.000000:0.000000:0.000000
las propiedades algebraicas de los números reales, y, muy particu-:@0.427979:0.904257:0.891725:0.904257:0.891725:0.887759:0.427979:0.887759:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
larmente, las enunciadas en el teorema precedente.:@0.427979:0.921607:0.790126:0.921607:0.790126:0.905110:0.427979:0.905110:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p x:@0.449389:0.189144:0.472083:0.189144:0.472083:0.172675:0.449389:0.172675:0.000000:0.000000:0.000000
( ):@0.458656:0.189028:0.478036:0.189028:0.478036:0.172531:0.458656:0.172531:0.000000:0.000000:0.000000
q x:@0.449427:0.205483:0.472026:0.205483:0.472026:0.189014:0.449427:0.189014:0.000000:0.000000:0.000000
( ):@0.458598:0.205367:0.477979:0.205367:0.477979:0.188869:0.458598:0.188869:0.000000:0.000000:0.000000
p:@0.681926:0.313201:0.691192:0.313201:0.691192:0.296732:0.681926:0.296732:0.000000
q:@0.681964:0.329539:0.691134:0.329539:0.691134:0.313070:0.681964:0.313070:0.000000
ps   qr:@0.746803:0.313556:0.796449:0.313556:0.796449:0.297088:0.746803:0.297088:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.766453:0.313441:0.777261:0.313441:0.777261:0.296943:0.766453:0.296943:0.000000
qs:@0.763968:0.329895:0.779284:0.329895:0.779284:0.313426:0.763968:0.313426:0.000000:0.000000
2:@0.510895:0.522351:0.519391:0.522351:0.519391:0.505854:0.510895:0.505854:0.000000
x :@0.497776:0.538806:0.509393:0.538806:0.509393:0.522337:0.497776:0.522337:0.000000:0.000000
– 1:@0.509393:0.538690:0.532530:0.538690:0.532530:0.522192:0.509393:0.522192:0.000000:0.000000:0.000000
2:@0.588863:0.657555:0.597359:0.657555:0.597359:0.641058:0.588863:0.641058:0.000000
x :@0.575782:0.674010:0.587399:0.674010:0.587399:0.657541:0.575782:0.657541:0.000000:0.000000
– 1:@0.587360:0.673894:0.610449:0.673894:0.610449:0.657396:0.587360:0.657396:0.000000:0.000000:0.000000
2:@0.500603:0.694265:0.509099:0.694265:0.509099:0.677767:0.500603:0.677767:0.000000
x :@0.487522:0.710719:0.499139:0.710719:0.499139:0.694250:0.487522:0.694250:0.000000:0.000000
– 1:@0.499100:0.710603:0.522189:0.710603:0.522189:0.694106:0.499100:0.694106:0.000000:0.000000:0.000000
x:@0.588730:0.694380:0.596205:0.694380:0.596205:0.677912:0.588730:0.677912:0.000000
( – 1)( + 1):@0.545653:0.710603:0.639282:0.710603:0.639282:0.694106:0.545653:0.694106:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.551606:0.710719:0.563223:0.710719:0.563223:0.694250:0.551606:0.694250:0.000000:0.000000
x :@0.598267:0.710719:0.609884:0.710719:0.609884:0.694250:0.598267:0.694250:0.000000:0.000000
2(:@0.667207:0.694265:0.681656:0.694265:0.681656:0.677767:0.667207:0.677767:0.000000:0.000000
x  – :@0.681656:0.694380:0.712406:0.694380:0.712406:0.677912:0.681656:0.677912:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.689131:0.687912:0.694084:0.687912:0.694084:0.678294:0.689131:0.678294:0.000000
1) +  (:@0.711442:0.694265:0.758411:0.694265:0.758411:0.677767:0.711442:0.677767:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x x – :@0.744983:0.694380:0.784207:0.694380:0.784207:0.677912:0.744983:0.677912:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1):@0.783244:0.694265:0.797693:0.694265:0.797693:0.677767:0.783244:0.677767:0.000000:0.000000
( – 1)( + 1):@0.685646:0.710603:0.779275:0.710603:0.779275:0.694106:0.685646:0.694106:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.691599:0.710719:0.703216:0.710719:0.703216:0.694250:0.691599:0.694250:0.000000:0.000000
x :@0.738260:0.710719:0.749877:0.710719:0.749877:0.694250:0.738260:0.694250:0.000000:0.000000
2:@0.491029:0.735132:0.499525:0.735132:0.499525:0.718634:0.491029:0.718634:0.000000
x  –     x  – x:@0.499525:0.735248:0.596084:0.735248:0.596084:0.718779:0.499525:0.718779:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.506999:0.728779:0.511952:0.728779:0.511952:0.719161:0.506999:0.719161:0.000000
2 +:@0.530274:0.735132:0.553719:0.735132:0.553719:0.718634:0.530274:0.718634:0.000000:0.000000:0.000000
2:@0.565336:0.728779:0.570289:0.728779:0.570289:0.719161:0.565336:0.719161:0.000000
( – 1)( + 1):@0.496733:0.751471:0.590362:0.751471:0.590362:0.734973:0.496733:0.734973:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.502686:0.751586:0.514303:0.751586:0.514303:0.735117:0.502686:0.735117:0.000000:0.000000
x :@0.549346:0.751586:0.560963:0.751586:0.560963:0.735117:0.549346:0.735117:0.000000:0.000000
3 + 2:@0.489037:0.773643:0.532596:0.773643:0.532596:0.757145:0.489037:0.757145:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.497533:0.773759:0.509150:0.773759:0.509150:0.757290:0.497533:0.757290:0.000000:0.000000
x :@0.493275:0.790097:0.504892:0.790097:0.504892:0.773629:0.493275:0.773629:0.000000:0.000000
+ 1:@0.504892:0.789982:0.528338:0.789982:0.528338:0.773484:0.504892:0.773484:0.000000:0.000000:0.000000
2:@0.598971:0.773643:0.607467:0.773643:0.607467:0.757145:0.598971:0.757145:0.000000
x :@0.585697:0.790097:0.597314:0.790097:0.597314:0.773629:0.585697:0.773629:0.000000:0.000000
+ 1:@0.597314:0.789982:0.620760:0.789982:0.620760:0.773484:0.597314:0.773484:0.000000:0.000000:0.000000
3:@0.632893:0.735132:0.641389:0.735132:0.641389:0.718634:0.632893:0.718634:0.000000
x  – x – :@0.641389:0.735248:0.697934:0.735248:0.697934:0.718779:0.641389:0.718779:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.648863:0.728779:0.653816:0.728779:0.653816:0.719161:0.648863:0.719161:0.000000
2:@0.697934:0.735132:0.706430:0.735132:0.706430:0.718634:0.697934:0.718634:0.000000
( – 1)( + 1):@0.622838:0.751471:0.716467:0.751471:0.716467:0.734973:0.622838:0.734973:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.628791:0.751586:0.640408:0.751586:0.640408:0.735117:0.628791:0.735117:0.000000:0.000000
x :@0.675452:0.751586:0.687069:0.751586:0.687069:0.735117:0.675452:0.735117:0.000000:0.000000
(:@0.747178:0.735132:0.753131:0.735132:0.753131:0.718634:0.747178:0.718634:0.000000
x – :@0.753131:0.735248:0.778927:0.735248:0.778927:0.718779:0.753131:0.718779:0.000000:0.000000:0.000000:0.000000
1)(3:@0.778927:0.735132:0.807825:0.735132:0.807825:0.718634:0.778927:0.718634:0.000000:0.000000:0.000000:0.000000
x + :@0.807825:0.735248:0.834469:0.735248:0.834469:0.718779:0.807825:0.718779:0.000000:0.000000:0.000000:0.000000
2):@0.834469:0.735132:0.848918:0.735132:0.848918:0.718634:0.834469:0.718634:0.000000:0.000000
( – 1)( + 1):@0.751224:0.751471:0.844853:0.751471:0.844853:0.734973:0.751224:0.734973:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.757177:0.751586:0.768793:0.751586:0.768793:0.735117:0.757177:0.735117:0.000000:0.000000
x :@0.803837:0.751586:0.815454:0.751586:0.815454:0.735117:0.803837:0.735117:0.000000:0.000000
x:@0.649910:0.657671:0.657385:0.657671:0.657385:0.641202:0.649910:0.641202:0.000000
x  :@0.633920:0.674010:0.650239:0.674016:0.650239:0.657547:0.633920:0.657541:0.000000:0.000000:0.000000
2:@0.641391:0.667616:0.646098:0.667616:0.646098:0.658015:0.641391:0.658015:0.000000
– 1:@0.650239:0.673900:0.673377:0.673900:0.673377:0.657402:0.650239:0.657402:0.000000:0.000000:0.000000
x:@0.516643:0.558710:0.524118:0.558710:0.524118:0.542241:0.516643:0.542241:0.000000
x:@0.500518:0.575049:0.507993:0.575049:0.507993:0.558580:0.500518:0.558580:0.000000
2:@0.508001:0.568587:0.512954:0.568587:0.512954:0.558969:0.508001:0.558969:0.000000
 – 1:@0.512954:0.574939:0.540234:0.574939:0.540234:0.558442:0.512954:0.558442:0.000000:0.000000:0.000000:0.000000
r:@0.715742:0.313201:0.721772:0.313201:0.721772:0.296732:0.715742:0.296732:0.000000
s:@0.715569:0.329539:0.721945:0.329539:0.721945:0.313070:0.715569:0.313070:0.000000
r x:@0.665187:0.189331:0.684645:0.189331:0.684645:0.172863:0.665187:0.172863:0.000000:0.000000:0.000000
( ):@0.671217:0.189216:0.690597:0.189216:0.690597:0.172718:0.671217:0.172718:0.000000:0.000000:0.000000
s x:@0.665013:0.205670:0.684818:0.205670:0.684818:0.189201:0.665013:0.189201:0.000000:0.000000:0.000000
( ):@0.671390:0.205554:0.690771:0.205554:0.690771:0.189057:0.671390:0.189057:0.000000:0.000000:0.000000
p x s x + q x r x:@0.577297:0.261245:0.698880:0.261245:0.698880:0.244776:0.577297:0.244776:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ) ( ) :@0.586563:0.261129:0.635844:0.261129:0.635844:0.244632:0.586563:0.244632:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ) ( ):@0.660041:0.261129:0.704833:0.261129:0.704833:0.244632:0.660041:0.244632:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
q x  s x:@0.611839:0.277584:0.664337:0.277584:0.664337:0.261115:0.611839:0.261115:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ) ( ):@0.621010:0.277468:0.670290:0.277468:0.670290:0.260970:0.621010:0.260970:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.199646:0.101454:0.307805:0.101454:0.307805:0.085981:0.199646:0.085981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cuáles son las propie-:@0.199884:0.130082:0.346196:0.130082:0.346196:0.115019:0.199884:0.115019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dades algebraicas y de orden de :@0.153341:0.145924:0.362834:0.145924:0.362834:0.130861:0.153341:0.130861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los números reales?:@0.153341:0.161766:0.277929:0.161766:0.277929:0.146703:0.153341:0.146703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Desequilibrio cognitivo:@0.199646:0.208760:0.363493:0.208760:0.363493:0.193288:0.199646:0.193288:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Es posible realizar una :@0.199884:0.237388:0.350488:0.237388:0.350488:0.222325:0.199884:0.222325:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
representación gráfica de la :@0.153341:0.253230:0.334639:0.253230:0.334639:0.238167:0.153341:0.238167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función real? :@0.153341:0.269072:0.239162:0.269072:0.239162:0.254009:0.153341:0.254009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000