56:@0.058194:0.966765:0.075166:0.966765:0.075166:0.950778:0.058194:0.950778:0.000000:0.000000
Función racional:@0.404235:0.116974:0.608228:0.116974:0.608228:0.072315:0.404235:0.072315:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.404235:0.160340:0.484318:0.160340:0.484318:0.143395:0.404235:0.143395:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean :@0.484320:0.159878:0.529016:0.159878:0.529016:0.143380:0.484320:0.143380:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p, q:@0.529016:0.159993:0.554022:0.159993:0.554022:0.143525:0.529016:0.143525:0.000000:0.000000:0.000000:0.000000
 dos funciones polinomiales. La función real  , :@0.554022:0.159878:0.879599:0.159878:0.879599:0.143380:0.554022:0.143380:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.868406:0.159993:0.872702:0.159993:0.872702:0.143525:0.868406:0.143525:0.000000
definida como:@0.404235:0.177229:0.508188:0.177229:0.508188:0.160731:0.404235:0.160731:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f =         q   0, :@0.508614:0.212046:0.608543:0.212046:0.608543:0.195577:0.508614:0.195577:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
≠ se llama función racional. :@0.578527:0.211930:0.791522:0.211930:0.791522:0.195432:0.578527:0.195432:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Nota que la función polinomial   no es nula. Además, de la definición :@0.404235:0.246632:0.895876:0.246632:0.895876:0.230134:0.404235:0.230134:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
q:@0.628343:0.246747:0.637514:0.246747:0.637514:0.230278:0.628343:0.230278:0.000000
de la función   se sigue que::@0.404235:0.263982:0.598058:0.263982:0.598058:0.247485:0.404235:0.247485:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.501156:0.264098:0.505452:0.264098:0.505452:0.247629:0.501156:0.247629:0.000000
f x:@0.539843:0.298799:0.557567:0.298799:0.557567:0.282331:0.539843:0.282331:0.000000:0.000000:0.000000
( ) =               ( ) ≠    :@0.544139:0.298684:0.707450:0.298684:0.707450:0.282186:0.544139:0.282186:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
q x:@0.636458:0.298799:0.659056:0.298799:0.659056:0.282331:0.636458:0.282331:0.000000:0.000000:0.000000
 0, x :@0.679959:0.298799:0.719067:0.298799:0.719067:0.282331:0.679959:0.282331:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.719067:0.298467:0.735115:0.298467:0.735115:0.283820:0.719067:0.283820:0.000000
 :@0.735104:0.298165:0.739502:0.298165:0.739502:0.284792:0.735104:0.284792:0.000000
:@0.739502:0.297715:0.753411:0.297715:0.753411:0.284268:0.739502:0.284268:0.000000
,:@0.753411:0.298684:0.756166:0.298684:0.756166:0.282186:0.753411:0.282186:0.000000
de la que obtenemos el dominio de la función  , es decir,:@0.404229:0.333385:0.803339:0.333385:0.803339:0.316888:0.404229:0.316888:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.736568:0.333501:0.740864:0.333501:0.740864:0.317032:0.736568:0.317032:0.000000
Dom (f) =  x :@0.545019:0.368202:0.637897:0.368202:0.637897:0.351734:0.545019:0.351734:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
{:@0.620423:0.368087:0.626280:0.368087:0.626280:0.351589:0.620423:0.351589:0.000000
:@0.637897:0.367870:0.653945:0.367870:0.653945:0.353223:0.637897:0.353223:0.000000
 :@0.653951:0.367568:0.658348:0.367568:0.658348:0.354195:0.653951:0.354195:0.000000
 :@0.658348:0.367118:0.677074:0.367118:0.677074:0.353671:0.658348:0.353671:0.000000:0.000000
|  ( ) ≠ 0}.:@0.677074:0.368087:0.750976:0.368087:0.750976:0.351589:0.677074:0.351589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
q x:@0.686225:0.368202:0.708823:0.368202:0.708823:0.351734:0.686225:0.351734:0.000000:0.000000:0.000000
Supongamos que   es un polinomio de grado  . Un número real   tal :@0.404240:0.402788:0.895908:0.402788:0.895908:0.386291:0.404240:0.386291:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
q:@0.531485:0.402904:0.540655:0.402904:0.540655:0.386435:0.531485:0.386435:0.000000
n:@0.728000:0.402739:0.736956:0.402739:0.736956:0.386986:0.728000:0.386986:0.000000
α:@0.857027:0.410375:0.867604:0.410375:0.867604:0.391376:0.857027:0.391376:0.000000
,:@0.867607:0.402904:0.870459:0.402904:0.870459:0.386435:0.867607:0.386435:0.000000
que   ( ) =  se llama raíz del polinomio  , con lo que   se expresa en :@0.404240:0.420139:0.895820:0.420139:0.895820:0.403641:0.404240:0.403641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
q:@0.438262:0.420255:0.447432:0.420255:0.447432:0.403786:0.438262:0.403786:0.000000
α:@0.453391:0.427725:0.463969:0.427725:0.463969:0.408726:0.453391:0.408726:0.000000
 0,:@0.484241:0.420255:0.498670:0.420255:0.498670:0.403786:0.484241:0.403786:0.000000:0.000000:0.000000
q:@0.692841:0.420255:0.702011:0.420255:0.702011:0.403786:0.692841:0.403786:0.000000
q:@0.786200:0.420255:0.795371:0.420255:0.795371:0.403786:0.786200:0.403786:0.000000
la forma   ( ) = (:@0.404232:0.437490:0.523484:0.437490:0.523484:0.420992:0.404232:0.420992:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
q x:@0.470254:0.437605:0.492852:0.437605:0.492852:0.421137:0.470254:0.421137:0.000000:0.000000:0.000000
  x –   r x ,  x :@0.513562:0.437605:0.625096:0.437605:0.625096:0.421137:0.513562:0.421137:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.548915:0.445076:0.559492:0.445076:0.559492:0.426077:0.548915:0.426077:0.000000
) ( )    :@0.559497:0.437490:0.613671:0.437490:0.613671:0.420992:0.559497:0.420992:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.624922:0.437273:0.640970:0.437273:0.640970:0.422626:0.624922:0.422626:0.000000
 :@0.640964:0.436971:0.645362:0.436971:0.645362:0.423598:0.640964:0.423598:0.000000
:@0.645162:0.436521:0.659072:0.436521:0.659072:0.423074:0.645162:0.423074:0.000000
, :@0.659072:0.437605:0.666065:0.437605:0.666065:0.421137:0.659072:0.421137:0.000000:0.000000
siendo   un polinomio de grado :@0.665873:0.437490:0.895878:0.437490:0.895878:0.420992:0.665873:0.420992:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r:@0.716829:0.437605:0.722859:0.437605:0.722859:0.421137:0.716829:0.421137:0.000000
n – :@0.404231:0.454956:0.431703:0.454956:0.431703:0.438487:0.404231:0.438487:0.000000:0.000000:0.000000:0.000000
1. Consecuentemente, el dominio de la función   está constituido :@0.431491:0.454841:0.895856:0.454841:0.895856:0.438343:0.431491:0.438343:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.770115:0.454956:0.774411:0.454956:0.774411:0.438487:0.770115:0.438487:0.000000
por todos los números reales que no son raíces del polinomio  . En :@0.404231:0.472191:0.895909:0.472191:0.895909:0.455694:0.404231:0.455694:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
q:@0.856926:0.472307:0.866096:0.472307:0.866096:0.455838:0.856926:0.455838:0.000000
particular, si  ( ) ≠ 0,        , se sigue que :@0.404231:0.489542:0.715543:0.489542:0.715543:0.473044:0.404231:0.473044:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
q x:@0.492175:0.489658:0.514773:0.489658:0.514773:0.473189:0.492175:0.473189:0.000000:0.000000:0.000000
∀:@0.563496:0.497129:0.575069:0.497129:0.575069:0.478129:0.563496:0.478129:0.000000
x:@0.575077:0.489658:0.582552:0.489658:0.582552:0.473189:0.575077:0.473189:0.000000
:@0.586693:0.489023:0.601346:0.489023:0.601346:0.475650:0.586693:0.475650:0.000000
:@0.605488:0.488455:0.618793:0.488455:0.618793:0.475593:0.605488:0.475593:0.000000
Dom (f) = :@0.715543:0.489658:0.790945:0.489658:0.790945:0.473189:0.715543:0.473189:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.790945:0.488573:0.804854:0.488573:0.804854:0.475127:0.790945:0.475127:0.000000
, y:@0.804854:0.489542:0.819573:0.489542:0.819573:0.473044:0.804854:0.473044:0.000000:0.000000:0.000000
f x:@0.404235:0.524359:0.421959:0.524359:0.421959:0.507891:0.404235:0.507891:0.000000:0.000000:0.000000
( ) =          ,             está bien definido. :@0.408531:0.524244:0.712457:0.524244:0.712457:0.507746:0.408531:0.507746:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∀:@0.503601:0.531830:0.515174:0.531830:0.515174:0.512831:0.503601:0.512831:0.000000
x:@0.515182:0.524359:0.522657:0.524359:0.522657:0.507891:0.515182:0.507891:0.000000
:@0.526798:0.523725:0.541451:0.523725:0.541451:0.510352:0.526798:0.510352:0.000000
:@0.545593:0.523157:0.558898:0.523157:0.558898:0.510294:0.545593:0.510294:0.000000
,  :@0.558898:0.524359:0.578317:0.524359:0.578317:0.507891:0.558898:0.507891:0.000000:0.000000:0.000000
Si   tiene como raíces reales  , …,   con :@0.404236:0.566073:0.700527:0.566073:0.700527:0.549575:0.404236:0.549576:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
q:@0.420072:0.566189:0.429242:0.566189:0.429242:0.549720:0.420072:0.549720:0.000000
α:@0.605809:0.573659:0.616387:0.573659:0.616387:0.554660:0.605809:0.554660:0.000000
1:@0.616390:0.569351:0.621343:0.569351:0.621343:0.559733:0.616390:0.559733:0.000000
α:@0.649960:0.573659:0.660538:0.573659:0.660538:0.554660:0.649960:0.554660:0.000000
k:@0.660543:0.569351:0.665406:0.569351:0.665406:0.559733:0.660543:0.559733:0.000000
k ≤ n:@0.700411:0.566188:0.736957:0.566188:0.736957:0.549720:0.700411:0.549720:0.000000:0.000000:0.000000:0.000000:0.000000
, el dominio de la fun-:@0.736957:0.566073:0.891734:0.566073:0.891734:0.549575:0.736957:0.549575:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ción    es el subconjunto de  ::@0.404227:0.583423:0.619840:0.583423:0.619840:0.566926:0.404227:0.566926:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.443412:0.583539:0.447709:0.583539:0.447709:0.567070:0.443412:0.567070:0.000000
:@0.603175:0.582455:0.617085:0.582455:0.617085:0.569008:0.603175:0.569008:0.000000
Dom (f) =  x :@0.485584:0.618241:0.578462:0.618241:0.578462:0.601772:0.485584:0.601772:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
{:@0.560988:0.618125:0.566845:0.618125:0.566845:0.601627:0.560988:0.601627:0.000000
:@0.578462:0.617908:0.594510:0.617908:0.594510:0.603261:0.578462:0.603261:0.000000
 :@0.594517:0.617606:0.598914:0.617606:0.598914:0.604233:0.594517:0.604233:0.000000
 :@0.598914:0.617156:0.617640:0.617156:0.617640:0.603709:0.598914:0.603709:0.000000:0.000000
|  ( ) ≠ 0} =     { , …,  },:@0.617640:0.618125:0.810409:0.618125:0.810409:0.601627:0.617640:0.601627:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
q x:@0.626791:0.618241:0.649389:0.618241:0.649389:0.601772:0.626791:0.601772:0.000000:0.000000:0.000000
:@0.707878:0.617156:0.721788:0.617156:0.721788:0.603709:0.707878:0.603709:0.000000
\:@0.726794:0.618125:0.732342:0.618125:0.728466:0.601627:0.722918:0.601627:0.000000
α:@0.741474:0.625711:0.752051:0.625711:0.752051:0.606712:0.741474:0.606712:0.000000
1:@0.752054:0.621403:0.757008:0.621403:0.757008:0.611785:0.752054:0.611785:0.000000
α:@0.786409:0.625711:0.796986:0.625711:0.796986:0.606712:0.786409:0.606712:0.000000
k:@0.796991:0.621470:0.801798:0.621470:0.801798:0.611869:0.796991:0.611869:0.000000
y la función   queda definida como::@0.404240:0.652827:0.655166:0.652827:0.655166:0.636329:0.404240:0.636329:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.491124:0.652942:0.495420:0.652942:0.495420:0.636473:0.491124:0.636473:0.000000
f x:@0.529233:0.687644:0.546957:0.687644:0.546957:0.671175:0.529233:0.671175:0.000000:0.000000:0.000000
( ) =          ,       :@0.533529:0.687528:0.644362:0.687528:0.644362:0.671030:0.533529:0.671030:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.632745:0.687644:0.640220:0.687644:0.640220:0.671175:0.632745:0.671175:0.000000
:@0.644362:0.687311:0.660410:0.687311:0.660410:0.672664:0.644362:0.672664:0.000000
 :@0.660404:0.687009:0.664801:0.687009:0.664801:0.673636:0.660404:0.673636:0.000000
:@0.664801:0.686559:0.678711:0.686559:0.678711:0.673112:0.664801:0.673112:0.000000
   { , …,  }.:@0.678711:0.687528:0.766772:0.687528:0.766772:0.671030:0.678711:0.671030:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
\:@0.683718:0.687528:0.689267:0.687528:0.685391:0.671030:0.679842:0.671030:0.000000
α:@0.698398:0.695114:0.708976:0.695114:0.708976:0.676115:0.698398:0.676115:0.000000
1:@0.708981:0.690806:0.713934:0.690806:0.713934:0.681188:0.708981:0.681188:0.000000
α:@0.742774:0.695114:0.753351:0.695114:0.753351:0.676115:0.742774:0.676115:0.000000
k:@0.753354:0.690873:0.758162:0.690873:0.758162:0.681272:0.753354:0.681272:0.000000
 :@0.404239:0.704879:0.408381:0.704879:0.408381:0.688381:0.404239:0.688381:0.000000
Más precisamente, como  (:@0.404239:0.722230:0.600995:0.722230:0.600995:0.705732:0.404239:0.705732:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
q:@0.585872:0.722345:0.595042:0.722345:0.595042:0.705876:0.585872:0.705876:0.000000
α:@0.601000:0.729816:0.611577:0.729816:0.611577:0.710817:0.601000:0.710817:0.000000
1:@0.611582:0.725507:0.616535:0.725507:0.616535:0.715889:0.611582:0.715889:0.000000
) = 0, … q:@0.616534:0.722345:0.684387:0.722345:0.684387:0.705876:0.616534:0.705876:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,  ( ) = 0, se sigue que   ( ):@0.668801:0.722230:0.868416:0.722230:0.868416:0.705732:0.668801:0.705732:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.690337:0.729816:0.700914:0.729816:0.700914:0.710817:0.690337:0.710817:0.000000
k:@0.700918:0.725575:0.705725:0.725575:0.705725:0.715974:0.700918:0.715974:0.000000
f:@0.836652:0.722345:0.840949:0.722345:0.840949:0.705876:0.836652:0.705876:0.000000
α:@0.846928:0.729816:0.857506:0.729816:0.857506:0.710817:0.846928:0.710817:0.000000
1:@0.857509:0.725507:0.862462:0.725507:0.862462:0.715889:0.857509:0.715889:0.000000
, …:@0.868416:0.722345:0.889010:0.722345:0.889010:0.705876:0.868416:0.705876:0.000000:0.000000:0.000000
,  :@0.889010:0.722230:0.895907:0.722230:0.895907:0.705732:0.889010:0.705732:0.000000:0.000000:0.000000
f:@0.404239:0.739696:0.408535:0.739696:0.408535:0.723227:0.404239:0.723227:0.000000
( ) no están definidos.:@0.408535:0.739580:0.574433:0.739580:0.574433:0.723083:0.408535:0.723083:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.414482:0.747167:0.425059:0.747167:0.425059:0.728168:0.414482:0.728168:0.000000
k:@0.425064:0.742926:0.429872:0.742926:0.429872:0.733324:0.425064:0.733324:0.000000
El gráfico de   se denota con  (  y se define como el conjunto:@0.404229:0.774282:0.847867:0.774282:0.847867:0.757784:0.404229:0.757784:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.494793:0.774397:0.499089:0.774397:0.499089:0.757929:0.494793:0.757929:0.000000
G f):@0.608244:0.774397:0.637084:0.774397:0.637084:0.757929:0.608244:0.757929:0.000000:0.000000:0.000000:0.000000
G f) =  (x,  f x:@0.517547:0.809099:0.613295:0.809099:0.613295:0.792630:0.517547:0.792630:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.528990:0.808983:0.534943:0.808983:0.534943:0.792486:0.528990:0.792486:0.000000
{:@0.565556:0.808983:0.571413:0.808983:0.571413:0.792486:0.565556:0.792486:0.000000
( )) | :@0.599867:0.808983:0.638494:0.808983:0.638494:0.792486:0.599867:0.792486:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.638494:0.809099:0.650111:0.809099:0.650111:0.792630:0.638494:0.792630:0.000000:0.000000
:@0.650111:0.808766:0.666159:0.808766:0.666159:0.794119:0.650111:0.794119:0.000000
 :@0.666165:0.808465:0.670562:0.808465:0.670562:0.795091:0.666165:0.795091:0.000000
:@0.670562:0.808015:0.684472:0.808015:0.684472:0.794568:0.670562:0.794568:0.000000
 \ { , …,  }}.:@0.684472:0.808983:0.778447:0.808983:0.778447:0.792486:0.684472:0.792486:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.704159:0.816570:0.714737:0.816570:0.714737:0.797571:0.704159:0.797571:0.000000
1:@0.714742:0.812261:0.719695:0.812261:0.719695:0.802643:0.714742:0.802643:0.000000
α:@0.748533:0.816570:0.759111:0.816570:0.759111:0.797571:0.748533:0.797571:0.000000
k:@0.759116:0.812261:0.763979:0.812261:0.763979:0.802643:0.759116:0.802643:0.000000
Igualdad de funciones racionales:@0.404235:0.845082:0.665807:0.845082:0.665807:0.827400:0.404235:0.827400:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean :@0.404235:0.861790:0.443167:0.861790:0.443167:0.845292:0.404235:0.845292:0.000000:0.000000:0.000000:0.000000:0.000000
p, q, r, s :@0.446937:0.861906:0.513928:0.861906:0.513928:0.845437:0.446937:0.845437:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
polinomios reales,   y :@0.517698:0.861790:0.685768:0.861790:0.685768:0.845292:0.517698:0.845292:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.660984:0.861906:0.665409:0.861906:0.665409:0.845437:0.660984:0.845437:0.000000
g :@0.689538:0.861906:0.701464:0.861906:0.701464:0.845437:0.689538:0.845437:0.000000:0.000000
dos funciones racionales :@0.705197:0.861790:0.896035:0.861790:0.896035:0.845292:0.705197:0.845292:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
definidas como::@0.404235:0.879141:0.520734:0.879141:0.520734:0.862643:0.404235:0.862643:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.487368:0.913958:0.505092:0.913958:0.505092:0.897489:0.487368:0.897489:0.000000:0.000000:0.000000
( ) =          ,   ( ) ≠ 0    ( )           ,    ( ) ≠ 0:@0.491664:0.913842:0.805804:0.913842:0.805804:0.897345:0.491664:0.897345:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
q x:@0.578454:0.913958:0.601053:0.913958:0.601053:0.897489:0.578454:0.897489:0.000000:0.000000:0.000000
,  g x  =:@0.634593:0.913958:0.695857:0.913958:0.695857:0.897489:0.634593:0.897489:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
s x:@0.752458:0.913958:0.772263:0.913958:0.772263:0.897489:0.752458:0.897489:0.000000:0.000000:0.000000
.:@0.805796:0.913842:0.808634:0.913842:0.808634:0.897345:0.805796:0.897345:0.000000
p:@0.537287:0.204956:0.546554:0.204956:0.546554:0.188487:0.537287:0.188487:0.000000
q:@0.537326:0.221294:0.546496:0.221294:0.546496:0.204826:0.537326:0.204826:0.000000
p(x):@0.585996:0.291598:0.613603:0.291598:0.613603:0.275129:0.585996:0.275129:0.000000:0.000000:0.000000:0.000000
q(x):@0.586035:0.307936:0.613546:0.307936:0.613546:0.291468:0.586035:0.291468:0.000000:0.000000:0.000000:0.000000
p x:@0.450614:0.517228:0.473308:0.517228:0.473308:0.500759:0.450614:0.500759:0.000000:0.000000:0.000000
( ):@0.459880:0.517112:0.479261:0.517112:0.479261:0.500615:0.459880:0.500615:0.000000:0.000000:0.000000
q x:@0.450652:0.533566:0.473250:0.533566:0.473250:0.517098:0.450652:0.517098:0.000000:0.000000:0.000000
( ):@0.459822:0.533451:0.479203:0.533451:0.479203:0.516953:0.459822:0.516953:0.000000:0.000000:0.000000
p x:@0.578632:0.680320:0.601326:0.680320:0.601326:0.663851:0.578632:0.663851:0.000000:0.000000:0.000000
( ):@0.587899:0.680204:0.607279:0.680204:0.607279:0.663707:0.587899:0.663707:0.000000:0.000000:0.000000
q x:@0.578671:0.696659:0.601269:0.696659:0.601269:0.680190:0.578671:0.680190:0.000000:0.000000:0.000000
( ):@0.587841:0.696543:0.607222:0.696543:0.607222:0.680045:0.587841:0.680045:0.000000:0.000000:0.000000
p x:@0.533900:0.906655:0.556594:0.906655:0.556594:0.890187:0.533900:0.890187:0.000000:0.000000:0.000000
( ):@0.543166:0.906540:0.562547:0.906540:0.562547:0.890042:0.543166:0.890042:0.000000:0.000000:0.000000
q x:@0.533938:0.922994:0.556536:0.922994:0.556536:0.906525:0.533938:0.906525:0.000000:0.000000:0.000000
( ):@0.543109:0.922878:0.562489:0.922878:0.562489:0.906381:0.543109:0.906381:0.000000:0.000000:0.000000
r x:@0.705640:0.906655:0.725098:0.906655:0.725098:0.890187:0.705640:0.890187:0.000000:0.000000:0.000000
( ):@0.711670:0.906540:0.731051:0.906540:0.731051:0.890042:0.711670:0.890042:0.000000:0.000000:0.000000
s x:@0.705467:0.922994:0.725272:0.922994:0.725272:0.906525:0.705467:0.906525:0.000000:0.000000:0.000000
( ):@0.711844:0.922878:0.731225:0.922878:0.731225:0.906381:0.711844:0.906381:0.000000:0.000000:0.000000
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 los métodos :@0.199884:0.130082:0.362555:0.130082:0.362555:0.115019:0.199884:0.115019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de resolución de ecuaciones :@0.153341:0.145924:0.340530:0.145924:0.340530:0.130861:0.153341:0.130861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
polinomiales y factorización de :@0.153341:0.161766:0.359068:0.161766:0.359068:0.146703:0.153341:0.146703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
polinomios?:@0.153341:0.177608:0.232510:0.177608:0.232510:0.162545:0.153341:0.162545:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Desequilibrio cognitivo:@0.199646:0.224760:0.363493:0.224760:0.363493:0.209287:0.199646:0.209287:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Por qué las funciones :@0.199884:0.253387:0.346600:0.253387:0.346600:0.238324:0.199884:0.238324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
polinomiales son las más senci-:@0.153341:0.269229:0.355867:0.269229:0.355867:0.254166:0.153341:0.254166:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
llas de evaluar?:@0.153341:0.285071:0.248485:0.285071:0.248485:0.270008:0.153341:0.270008:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.43. Graficar funciones racionales con cocientes de polinomios de grado ≤3 en diversos ejemplos, y determinar las ecuaciones de las asíntotas, si las tuvieran, con ayuda de la TIC.:@0.142897:0.940354:0.874146:0.940354:0.874146:0.930312:0.142897:0.930312:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.44. Determinar el dominio, rango, ceros, paridad, monotonía, extremos y asíntotas de funciones racionales con cocientes de polinomios de grado ≤3 con apoyo de las TIC. :@0.142897:0.949155:0.894398:0.949155:0.894398:0.939113:0.142897:0.939113:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.200180:0.406128:0.297803:0.406128:0.297803:0.390655:0.200180:0.390655:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.200180:0.418696:0.284243:0.418696:0.284243:0.403223:0.200180:0.403223:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Como sabemos, las :@0.200418:0.443170:0.329334:0.443170:0.329334:0.428107:0.200418:0.428107:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
funciones reales más sencillas :@0.153875:0.459012:0.347520:0.459012:0.347520:0.443949:0.153875:0.443949:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de evaluar son las funciones po-:@0.153875:0.474854:0.361771:0.474854:0.361771:0.459791:0.153875:0.459791:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
linomiales que tienen la forma:@0.153875:0.490696:0.349617:0.490696:0.349617:0.475633:0.153875:0.475633:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p x:@0.153875:0.513773:0.174596:0.513773:0.174596:0.498736:0.153875:0.498736:0.000000:0.000000:0.000000
( ) =:@0.162336:0.513667:0.193681:0.513667:0.193681:0.498604:0.162336:0.498604:0.000000:0.000000:0.000000:0.000000:0.000000
 a  + a x:@0.193681:0.513773:0.249437:0.513772:0.249437:0.498735:0.193681:0.498736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.205663:0.516658:0.210186:0.516658:0.210186:0.507876:0.205663:0.507876:0.000000
1   :@0.235885:0.516658:0.251640:0.516658:0.251640:0.507876:0.235885:0.507876:0.000000:0.000000:0.000000:0.000000
+ … + :@0.251642:0.513666:0.296461:0.513666:0.296461:0.498603:0.251642:0.498603:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a x ,:@0.296461:0.513772:0.323652:0.513772:0.323652:0.498735:0.296461:0.498735:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.304516:0.516719:0.309500:0.516719:0.309500:0.507953:0.304516:0.507953:0.000000
n:@0.316229:0.507927:0.321213:0.507927:0.321213:0.499161:0.316229:0.499161:0.000000
x :@0.153873:0.529614:0.164480:0.529614:0.164480:0.514577:0.153873:0.514577:0.000000:0.000000
:@0.164486:0.529159:0.178441:0.529159:0.178441:0.516423:0.164486:0.516423:0.000000
 :@0.178441:0.529310:0.182838:0.529310:0.182838:0.515937:0.178441:0.515937:0.000000
:@0.182838:0.528505:0.194933:0.528505:0.194933:0.516812:0.182838:0.516812:0.000000
,:@0.194933:0.529508:0.197449:0.529508:0.197449:0.514445:0.194933:0.514445:0.000000
donde   :@0.153878:0.552479:0.214369:0.552478:0.214369:0.537414:0.153878:0.537416:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.200474:0.552584:0.208671:0.552584:0.208671:0.537548:0.200474:0.537548:0.000000
i:@0.208567:0.555532:0.210587:0.555532:0.210587:0.546766:0.208567:0.546766:0.000000
:@0.214368:0.552129:0.228323:0.552129:0.228323:0.539392:0.214368:0.539392:0.000000
 :@0.228323:0.552280:0.232720:0.552280:0.232720:0.538906:0.228323:0.538906:0.000000
:@0.232720:0.551475:0.244815:0.551475:0.244815:0.539782:0.232720:0.539782:0.000000
, :@0.244815:0.552478:0.251113:0.552478:0.251113:0.537414:0.244815:0.537414:0.000000:0.000000
i = :@0.251113:0.552583:0.272080:0.552583:0.272080:0.537546:0.251113:0.537546:0.000000:0.000000:0.000000:0.000000
0, 1:@0.272080:0.552478:0.293891:0.552478:0.293891:0.537414:0.272080:0.537414:0.000000:0.000000:0.000000:0.000000
, …, n.:@0.293891:0.552583:0.330408:0.552583:0.330408:0.537546:0.293891:0.537546:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.330408:0.552478:0.334190:0.552478:0.334190:0.537414:0.330408:0.537414:0.000000
Para calcular  ( ) con   :@0.153875:0.575448:0.307772:0.575448:0.307772:0.560385:0.153875:0.560385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p x:@0.238837:0.575554:0.259558:0.575554:0.259558:0.560517:0.238837:0.560517:0.000000:0.000000:0.000000
x:@0.297165:0.575554:0.303990:0.575554:0.303990:0.560517:0.297165:0.560517:0.000000
:@0.307773:0.575098:0.321727:0.575098:0.321727:0.562362:0.307773:0.562362:0.000000
 :@0.321727:0.575249:0.326125:0.575249:0.326125:0.561876:0.321727:0.561876:0.000000
:@0.326125:0.574444:0.338220:0.574444:0.338220:0.562752:0.326125:0.562752:0.000000
, :@0.338220:0.575447:0.344517:0.575447:0.344517:0.560384:0.338220:0.560384:0.000000:0.000000
se aplica el esquema de Hörner. :@0.153877:0.591289:0.361082:0.591289:0.361082:0.576226:0.153877:0.576226:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Esto es,  ( ) se escribe como:@0.153877:0.607131:0.339481:0.607131:0.339481:0.592068:0.153877:0.592068:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p x:@0.204956:0.607237:0.225677:0.607237:0.225677:0.592200:0.204956:0.592200:0.000000:0.000000:0.000000
p x:@0.153877:0.630208:0.174598:0.630208:0.174598:0.615171:0.153877:0.615171:0.000000:0.000000:0.000000
( ) = :@0.162337:0.630102:0.197465:0.630102:0.197465:0.615039:0.162337:0.615039:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a +x(a +…x(a + a x)…):@0.197465:0.630208:0.358953:0.630208:0.358953:0.615171:0.197465:0.615171:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.205663:0.633094:0.210186:0.633094:0.210186:0.624312:0.205663:0.624312:0.000000
1:@0.240106:0.633155:0.244403:0.633155:0.244403:0.624389:0.240106:0.624389:0.000000
n–1:@0.287938:0.633155:0.302561:0.633155:0.302561:0.624389:0.287938:0.624389:0.000000:0.000000:0.000000
n:@0.324337:0.633155:0.329321:0.633155:0.329321:0.624389:0.324337:0.624389:0.000000
,:@0.358953:0.630102:0.361468:0.630102:0.361468:0.615039:0.358953:0.615039:0.000000
lo que facilita el cálculo redu-:@0.153888:0.653073:0.343804:0.653073:0.343804:0.638010:0.153888:0.638010:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ciendo el número de operacio-:@0.153888:0.668915:0.354448:0.668915:0.354448:0.653852:0.153888:0.653852:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nes elementales.:@0.153888:0.684757:0.259479:0.684757:0.259479:0.669694:0.153888:0.669694:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En orden de complejidad, :@0.153888:0.707728:0.323912:0.707728:0.323912:0.692665:0.153888:0.692665:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
siguen las funciones racionales. :@0.153888:0.723570:0.357419:0.723570:0.357419:0.708507:0.153888:0.708507:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Estas son funciones reales. Lo :@0.153888:0.739412:0.346691:0.739412:0.346691:0.724349:0.153888:0.724349:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que nos interesa es determinar :@0.153888:0.755254:0.356189:0.755254:0.356189:0.740191:0.153888:0.740191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
su dominio y, si es posible, su :@0.153888:0.771096:0.345440:0.771096:0.345440:0.756033:0.153888:0.756033:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
recorrido.:@0.153888:0.786938:0.216032:0.786938:0.216032:0.771875:0.153888:0.771875:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000