144:@0.031627:0.974518:0.062330:0.974518:0.062330:0.956333:0.031627:0.956333:0.000000:0.000000:0.000000
Factorización y fracciones algebraicas:@0.073089:0.043661:0.408833:0.043661:0.408833:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una ecuación fraccionaria es aquella que incluye números fraccionarios o en la que la :@0.305399:0.238452:0.922902:0.238452:0.922902:0.222018:0.305399:0.222018:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
incógnita es parte de una fracción.:@0.305399:0.255094:0.555771:0.255094:0.555771:0.238660:0.305399:0.238660:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para resolver una ecuación fraccionaria, se pueden seguir los siguientes pasos::@0.305399:0.278878:0.869511:0.278878:0.869511:0.262444:0.305399:0.262444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.  Se halla el denominador común de las fracciones que hacen parte de la ecuación.:@0.305399:0.302673:0.917926:0.302673:0.917926:0.286240:0.305399:0.286240:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.  Se multiplican los términos de la ecuación por el denominador común.:@0.305399:0.326462:0.850525:0.326462:0.850525:0.310029:0.305399:0.310029:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3.  Se simplifican las fracciones (se eliminan los denominadores).:@0.305399:0.350253:0.778705:0.350253:0.778705:0.333819:0.305399:0.333819:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4.  Se resuelve la ecuación como una ecuación lineal.:@0.305399:0.374042:0.697463:0.374042:0.697463:0.357608:0.305399:0.357608:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5.  Se verifica la validez de la respuesta.:@0.305399:0.397831:0.594528:0.397831:0.594528:0.381397:0.305399:0.381397:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 1:@0.293652:0.436842:0.369434:0.436842:0.369434:0.420172:0.293652:0.420172:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Resuelve :@0.293652:0.470417:0.361983:0.470417:0.361983:0.453983:0.293652:0.453983:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.376637:0.464311:0.385619:0.464311:0.385619:0.447877:0.376637:0.447877:0.000000
x:@0.364249:0.478290:0.371704:0.478290:0.371704:0.461884:0.364249:0.461884:0.000000
2:@0.371630:0.477735:0.386963:0.477735:0.386963:0.464020:0.371630:0.464020:0.000000
1:@0.386871:0.478290:0.395854:0.478290:0.395854:0.461856:0.386871:0.461856:0.000000
1:@0.400308:0.469872:0.415642:0.469872:0.415642:0.456156:0.400308:0.456156:0.000000
12:@0.425864:0.464311:0.443756:0.464311:0.443756:0.447877:0.425864:0.447877:0.000000:0.000000
x:@0.417912:0.478290:0.425367:0.478290:0.425367:0.461884:0.417912:0.461884:0.000000
2:@0.425294:0.477735:0.440627:0.477735:0.440627:0.464020:0.425294:0.464020:0.000000
2:@0.440535:0.478290:0.449518:0.478290:0.449518:0.461856:0.440535:0.461856:0.000000
5:@0.453972:0.469872:0.469305:0.469872:0.469305:0.456156:0.453972:0.456156:0.000000
9:@0.483994:0.464311:0.492977:0.464311:0.492977:0.447877:0.483994:0.447877:0.000000
x:@0.471606:0.478290:0.479061:0.478290:0.479061:0.461884:0.471606:0.461884:0.000000
2:@0.478988:0.477735:0.494321:0.477735:0.494321:0.464020:0.478988:0.464020:0.000000
1:@0.494229:0.478290:0.503212:0.478290:0.503212:0.461856:0.494229:0.461856:0.000000
Los denominadores son binomios. El común denominador es el producto de los factores :@0.293663:0.499578:0.931337:0.499578:0.931337:0.483144:0.293663:0.483144:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que conforman los denominadores. En este caso, es (:@0.293663:0.516220:0.677576:0.516220:0.677576:0.499786:0.293663:0.499786:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.677197:0.516220:0.684652:0.516220:0.684652:0.499814:0.677197:0.499814:0.000000
2:@0.684578:0.515665:0.699912:0.515665:0.699912:0.501949:0.684578:0.501949:0.000000
1)(:@0.699820:0.516220:0.718411:0.516220:0.718411:0.499786:0.699820:0.499786:0.000000:0.000000:0.000000
x:@0.718319:0.516220:0.725774:0.516220:0.725774:0.499814:0.718319:0.499814:0.000000
1:@0.725700:0.515665:0.741033:0.515665:0.741033:0.501949:0.725700:0.501949:0.000000
2).:@0.740941:0.516220:0.757858:0.516220:0.757858:0.499786:0.740941:0.499786:0.000000:0.000000:0.000000
Multiplicamos todos los términos de la ecuación por el denominador común::@0.293663:0.545371:0.853881:0.545371:0.853881:0.528937:0.293663:0.528937:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.414629:0.572832:0.423612:0.572832:0.423612:0.556398:0.414629:0.556398:0.000000
x:@0.402241:0.586811:0.409696:0.586811:0.409696:0.570405:0.402241:0.570405:0.000000
2:@0.409622:0.586257:0.424956:0.586257:0.424956:0.572541:0.409622:0.572541:0.000000
1:@0.424864:0.586811:0.433846:0.586811:0.433846:0.570377:0.424864:0.570377:0.000000
 (:@0.438301:0.578948:0.447136:0.578948:0.447136:0.562514:0.438301:0.562514:0.000000:0.000000
x:@0.447044:0.578948:0.454499:0.578948:0.454499:0.562542:0.447044:0.562542:0.000000
2:@0.454426:0.578393:0.469759:0.578393:0.469759:0.564678:0.454426:0.564678:0.000000
1)(:@0.469667:0.578948:0.488258:0.578948:0.488258:0.562514:0.469667:0.562514:0.000000:0.000000:0.000000
x:@0.488166:0.578948:0.495621:0.578948:0.495621:0.562542:0.488166:0.562542:0.000000
1 1 :@0.495548:0.578393:0.548284:0.578393:0.548284:0.564678:0.495548:0.564678:0.000000:0.000000:0.000000:0.000000
2) :@0.510789:0.578948:0.528533:0.578948:0.528533:0.562514:0.510789:0.562514:0.000000:0.000000:0.000000
12:@0.558520:0.572832:0.576412:0.572832:0.576412:0.556398:0.558520:0.556398:0.000000:0.000000
x:@0.550568:0.586811:0.558023:0.586811:0.558023:0.570405:0.550568:0.570405:0.000000
1:@0.557950:0.586257:0.573283:0.586257:0.573283:0.572541:0.557950:0.572541:0.000000
2:@0.573191:0.586811:0.582174:0.586811:0.582174:0.570377:0.573191:0.570377:0.000000
 (:@0.586628:0.578948:0.595464:0.578948:0.595464:0.562514:0.586628:0.562514:0.000000:0.000000
x:@0.595372:0.578948:0.602827:0.578948:0.602827:0.562542:0.595372:0.562542:0.000000
2:@0.602753:0.578393:0.618086:0.578393:0.618086:0.564678:0.602753:0.564678:0.000000
1)(:@0.617994:0.578948:0.636586:0.578948:0.636586:0.562514:0.617994:0.562514:0.000000:0.000000:0.000000
x:@0.636494:0.578948:0.643948:0.578948:0.643948:0.562542:0.636494:0.562542:0.000000
1 5:@0.643875:0.578393:0.692102:0.578393:0.692102:0.564678:0.643875:0.564678:0.000000:0.000000:0.000000
2)   :@0.659116:0.578948:0.696041:0.578948:0.696041:0.562514:0.659116:0.562514:0.000000:0.000000:0.000000:0.000000:0.000000
9:@0.710755:0.572832:0.719738:0.572832:0.719738:0.556398:0.710755:0.556398:0.000000
x:@0.698367:0.586811:0.705822:0.586811:0.705822:0.570405:0.698367:0.570405:0.000000
2:@0.705748:0.586257:0.721082:0.586257:0.721082:0.572541:0.705748:0.572541:0.000000
1:@0.720990:0.586811:0.729972:0.586811:0.729972:0.570377:0.720990:0.570377:0.000000
 (:@0.734427:0.578948:0.743262:0.578948:0.743262:0.562514:0.734427:0.562514:0.000000:0.000000
x:@0.743170:0.578948:0.750625:0.578948:0.750625:0.562542:0.743170:0.562542:0.000000
2:@0.750552:0.578393:0.765885:0.578393:0.765885:0.564678:0.750552:0.564678:0.000000
1)(:@0.765793:0.578948:0.784384:0.578948:0.784384:0.562514:0.765793:0.562514:0.000000:0.000000:0.000000
x:@0.784292:0.578948:0.791747:0.578948:0.791747:0.562542:0.784292:0.562542:0.000000
1:@0.791673:0.578393:0.807007:0.578393:0.807007:0.564678:0.791673:0.564678:0.000000
2):@0.806915:0.578948:0.820702:0.578948:0.820702:0.562514:0.806915:0.562514:0.000000:0.000000
Al simplificar los términos, obtenemos::@0.293647:0.608099:0.573244:0.608099:0.573244:0.591665:0.293647:0.591665:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3(:@0.496311:0.637250:0.510098:0.637250:0.510098:0.620816:0.496311:0.620816:0.000000:0.000000
x :@0.510006:0.637250:0.520700:0.637250:0.520700:0.620844:0.510006:0.620844:0.000000:0.000000
1  1 :@0.520645:0.636695:0.577892:0.636695:0.577892:0.622979:0.520645:0.622979:0.000000:0.000000:0.000000:0.000000:0.000000
2) :@0.540396:0.637250:0.558141:0.637250:0.558141:0.620816:0.540396:0.620816:0.000000:0.000000:0.000000
12(:@0.577800:0.637250:0.600496:0.637250:0.600496:0.620816:0.577800:0.620816:0.000000:0.000000:0.000000
x :@0.600404:0.637250:0.611098:0.637250:0.611098:0.620844:0.600404:0.620844:0.000000:0.000000
2  5:@0.611043:0.636695:0.663780:0.636695:0.663780:0.622979:0.611043:0.622979:0.000000:0.000000:0.000000:0.000000
1)   9(:@0.630794:0.637250:0.681432:0.637250:0.681432:0.620816:0.630794:0.620816:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x   :@0.681340:0.637250:0.710534:0.637250:0.710534:0.620844:0.681340:0.620844:0.000000:0.000000:0.000000:0.000000
1:@0.691980:0.636695:0.707313:0.636695:0.707313:0.622979:0.691980:0.622979:0.000000
2):@0.710461:0.637250:0.724248:0.637250:0.724248:0.620816:0.710461:0.620816:0.000000:0.000000
Resolviendo los productos y reduciendo términos semejantes, obtenemos::@0.293647:0.666401:0.835264:0.666401:0.835264:0.649967:0.293647:0.649967:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3    6   12    12   9:@0.503563:0.695552:0.673315:0.695552:0.673315:0.679118:0.503563:0.679118:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.512472:0.695552:0.519927:0.695552:0.519927:0.679146:0.512472:0.679146:0.000000
1 1:@0.523811:0.694997:0.571191:0.694997:0.571191:0.681281:0.523811:0.681281:0.000000:0.000000:0.000000
x:@0.592857:0.695552:0.600312:0.695552:0.600312:0.679146:0.592857:0.679146:0.000000
2:@0.604196:0.694997:0.619529:0.694997:0.619529:0.681281:0.604196:0.681281:0.000000
5:@0.645133:0.694997:0.660466:0.694997:0.660466:0.681281:0.645133:0.681281:0.000000
x  :@0.673223:0.695552:0.699159:0.695552:0.699159:0.679146:0.673223:0.679146:0.000000:0.000000:0.000000
1:@0.680604:0.694997:0.695937:0.694997:0.695937:0.681281:0.680604:0.681281:0.000000
18:@0.699085:0.695552:0.716977:0.695552:0.716977:0.679118:0.699085:0.679118:0.000000:0.000000
15    6  9    18:@0.543378:0.724703:0.677125:0.724703:0.677125:0.708269:0.543378:0.708269:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.561178:0.724703:0.568633:0.724703:0.568633:0.708297:0.561178:0.708297:0.000000
2 5:@0.572517:0.724148:0.615939:0.724148:0.615939:0.710432:0.572517:0.710432:0.000000:0.000000:0.000000
x:@0.628696:0.724703:0.636151:0.724703:0.636151:0.708297:0.628696:0.708297:0.000000
1:@0.640034:0.724148:0.655368:0.724148:0.655368:0.710432:0.640034:0.710432:0.000000
15    6   9:@0.470614:0.753854:0.559981:0.753854:0.559981:0.737420:0.470614:0.737420:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.488414:0.753854:0.495869:0.753854:0.495869:0.737448:0.488414:0.737448:0.000000
2 2:@0.499753:0.753299:0.547133:0.753299:0.547133:0.739583:0.499753:0.739583:0.000000:0.000000:0.000000
x   :@0.559889:0.753854:0.589083:0.753854:0.589083:0.737448:0.559889:0.737448:0.000000:0.000000:0.000000:0.000000
1 5:@0.570529:0.753299:0.617191:0.753299:0.617191:0.739583:0.570529:0.739583:0.000000:0.000000:0.000000
6   9    18   9    6:@0.589010:0.753854:0.749834:0.753854:0.749834:0.737420:0.589010:0.737420:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.629947:0.753854:0.637402:0.753854:0.637402:0.737448:0.629947:0.737448:0.000000
1:@0.641286:0.753299:0.656619:0.753299:0.656619:0.739583:0.641286:0.739583:0.000000
2:@0.682224:0.753299:0.697557:0.753299:0.697557:0.739583:0.682224:0.739583:0.000000
x:@0.710313:0.753854:0.717768:0.753854:0.717768:0.737448:0.710313:0.737448:0.000000
1:@0.721652:0.753299:0.736985:0.753299:0.736985:0.739583:0.721652:0.739583:0.000000
6    24:@0.581536:0.783005:0.638875:0.783005:0.638875:0.766571:0.581536:0.766571:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.590445:0.783005:0.597900:0.783005:0.597900:0.766599:0.590445:0.766599:0.000000
5:@0.601784:0.782450:0.617117:0.782450:0.617117:0.768734:0.601784:0.768734:0.000000
Luego, al dividir entre 6 cada término de la igualdad, obtenemos:@0.293573:0.812156:0.760755:0.812156:0.760755:0.795722:0.293573:0.795722:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.590445:0.841306:0.597900:0.841306:0.597900:0.824900:0.590445:0.824900:0.000000
   4:@0.597827:0.841306:0.629966:0.841306:0.629966:0.824873:0.597827:0.824873:0.000000:0.000000:0.000000:0.000000
5:@0.601784:0.840752:0.617117:0.840752:0.617117:0.827036:0.601784:0.827036:0.000000
Tema 8. Ecuaciones con fracciones algebraicas:@0.073089:0.098522:0.755255:0.098522:0.755255:0.067281:0.073089:0.067281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Las ecuaciones fraccionarias :@0.078672:0.295074:0.263125:0.295074:0.263125:0.280134:0.078672:0.280134:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
son muy útiles en varias :@0.078672:0.308942:0.235763:0.308942:0.235763:0.294002:0.078672:0.294002:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ramas de las ciencias. :@0.078672:0.322810:0.218663:0.322810:0.218663:0.307870:0.078672:0.307870:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Por ejemplo, si se quiere :@0.078672:0.336678:0.237507:0.336678:0.237507:0.321738:0.078672:0.321738:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
determinar la longitud focal :@0.078672:0.350546:0.260979:0.350546:0.260979:0.335607:0.078672:0.335607:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de una lente, se utiliza la :@0.078672:0.364415:0.238233:0.364415:0.238233:0.349475:0.078672:0.349475:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
expresión:@0.078672:0.378283:0.141804:0.378283:0.141804:0.363343:0.078672:0.363343:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.081350:0.393308:0.090333:0.393308:0.090333:0.376875:0.081350:0.376875:0.000000
f:@0.081037:0.407287:0.085731:0.407287:0.085731:0.390881:0.081037:0.390881:0.000000
5 2:@0.092938:0.398598:0.133166:0.398598:0.133166:0.386130:0.092938:0.386130:0.000000:0.000000:0.000000
(:@0.106626:0.399103:0.111061:0.399103:0.111061:0.384163:0.106626:0.384163:0.000000
n:@0.110827:0.399103:0.119461:0.399103:0.119461:0.384188:0.110827:0.384188:0.000000
1)(:@0.132915:0.399103:0.149482:0.399103:0.149482:0.384163:0.132915:0.384163:0.000000:0.000000:0.000000
1:@0.157426:0.393308:0.166409:0.393308:0.166409:0.376875:0.157426:0.376875:0.000000
R:@0.154868:0.407287:0.163814:0.407287:0.163814:0.390881:0.154868:0.390881:0.000000
1:@0.163738:0.410455:0.168975:0.410455:0.168975:0.400874:0.163738:0.400874:0.000000
 +:@0.174533:0.399103:0.187937:0.399103:0.187937:0.384163:0.174533:0.384163:0.000000:0.000000
1:@0.195887:0.393308:0.204870:0.393308:0.204870:0.376875:0.195887:0.376875:0.000000
R:@0.193329:0.407287:0.202275:0.407287:0.202275:0.390881:0.193329:0.390881:0.000000
2:@0.202199:0.410455:0.207436:0.410455:0.207436:0.400874:0.202199:0.400874:0.000000
 ) :@0.212995:0.399103:0.224524:0.399103:0.224524:0.384163:0.212995:0.384163:0.000000:0.000000:0.000000
Donde f es la distancia focal, :@0.078672:0.420119:0.263096:0.420119:0.263096:0.405179:0.078672:0.405179:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n es el índice de refracción :@0.078672:0.433988:0.253266:0.433988:0.253266:0.419048:0.078672:0.419048:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la lente, y   y   los :@0.078672:0.447856:0.226350:0.447854:0.226350:0.432915:0.078672:0.432916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.162006:0.447856:0.170139:0.447856:0.170139:0.432941:0.162006:0.432941:0.000000
1:@0.169915:0.450738:0.174676:0.450738:0.174676:0.442028:0.169915:0.442028:0.000000
R:@0.188508:0.447854:0.196641:0.447854:0.196641:0.432940:0.188508:0.432940:0.000000
2:@0.196411:0.450738:0.201172:0.450738:0.201172:0.442028:0.196411:0.442028:0.000000
radios de las esferas que :@0.078673:0.461723:0.237705:0.461723:0.237705:0.446783:0.078673:0.446783:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
forman la lente.:@0.078673:0.475591:0.178533:0.475591:0.178533:0.460651:0.078673:0.460651:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinariedad :@0.078673:0.235457:0.231059:0.235457:0.231059:0.220050:0.078673:0.220050:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática  :@0.078673:0.250586:0.164167:0.250586:0.164167:0.235646:0.078673:0.235646:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y física :@0.078673:0.265715:0.125578:0.265715:0.125578:0.250775:0.078673:0.250775:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Resuelve la siguiente ecuación para  : :@0.293660:0.182024:0.569553:0.182024:0.569553:0.165590:0.293660:0.165590:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.555011:0.182024:0.562466:0.182024:0.562466:0.165618:0.555011:0.165618:0.000000
x:@0.581238:0.175914:0.588693:0.175914:0.588693:0.159508:0.581238:0.159508:0.000000
2:@0.580465:0.189893:0.589448:0.189893:0.589448:0.173460:0.580465:0.173460:0.000000
   :@0.600363:0.182030:0.623593:0.182030:0.623593:0.165596:0.600363:0.165596:0.000000:0.000000:0.000000
5:@0.604321:0.181475:0.619654:0.181475:0.619654:0.167760:0.604321:0.167760:0.000000
3:@0.631808:0.175914:0.640791:0.175914:0.640791:0.159480:0.631808:0.159480:0.000000
4:@0.631808:0.189893:0.640791:0.189893:0.640791:0.173460:0.631808:0.173460:0.000000
a b:@0.127367:0.155346:0.161052:0.155346:0.161052:0.138940:0.127367:0.138940:0.000000:0.000000:0.000000
1:@0.136552:0.154792:0.151885:0.154792:0.151885:0.141076:0.136552:0.141076:0.000000
3:@0.135116:0.169326:0.144099:0.169326:0.144099:0.152892:0.135116:0.152892:0.000000
a:@0.144026:0.169326:0.153284:0.169326:0.153284:0.152920:0.144026:0.152920:0.000000
1:@0.163537:0.160145:0.178870:0.160145:0.178870:0.146429:0.163537:0.146429:0.000000
a b:@0.181369:0.155346:0.215054:0.155346:0.215054:0.138940:0.181369:0.138940:0.000000:0.000000:0.000000
2:@0.190554:0.154792:0.205888:0.154792:0.205888:0.141076:0.190554:0.141076:0.000000
2:@0.189119:0.169326:0.198101:0.169326:0.198101:0.152892:0.189119:0.152892:0.000000
b:@0.198028:0.169326:0.207287:0.169326:0.207287:0.152920:0.198028:0.152920:0.000000
Reto matemático:@0.302768:0.139665:0.425244:0.139665:0.425244:0.124259:0.302768:0.124259:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DBA 9 (Ev. 4) Describe diferentes usos del signo igual (equivalencia, igualdad condicionada) en las expresiones algebraicas.:@0.230369:0.965693:0.873471:0.965693:0.873471:0.953741:0.230369:0.953741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DBA 10 (Ev. 1)Toma decisiones informadas en exploraciones numéricas, algebraicas o gráficas de los modelos matemáticos usados.:@0.230369:0.976409:0.918266:0.976409:0.918266:0.964457:0.230369:0.964457:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Distancia focal:@0.079891:0.518236:0.105884:0.518236:0.105884:0.514335:0.079891:0.514335:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Angulo de visión:@0.165929:0.483248:0.196071:0.483248:0.196071:0.479347:0.165929:0.479347:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Plano focal:@0.080388:0.527063:0.100010:0.527063:0.100010:0.523162:0.080388:0.523162:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000