Resuelva la expresión (3y²+2y-3/y²+4y+4-5y+4/y+2)*(5y+2/y²-9+y-6/y-3)
por favor me pueden ayudar con el desarrollo completo
Ccfh:
El y+2 en el primer parentesis, esta dividiendo TODA la expresion que cominza con "y^2"?
Respuestas
Respuesta dada por:
2
Si he entendido bien el enunciado:
![(\frac{3y^2+2y-3}{y^2+4y+4}- \frac{5y+4}{y+2})*( \frac{5y+2}{y^2-9}+ \frac{y-6}{y-3})=\\ \\=(\frac{3y^2+2y-3}{(y+2)^2}- \frac{5y+4}{y+2}* \frac{y+2}{y+2} )*( \frac{5y+2}{(y-3)(y+3)}+ \frac{y-6}{y-3}* \frac{y+3}{y+3})=\\=(\frac{3y^2+2y-3}{(y+2)^2}- \frac{(5y+4)(y+2)}{(y+2)^2} )*( \frac{5y+2}{(y-3)(y+3)}+ \frac{(y-6)(y+3)}{(y-3)(y+3)})= (\frac{3y^2+2y-3}{y^2+4y+4}- \frac{5y+4}{y+2})*( \frac{5y+2}{y^2-9}+ \frac{y-6}{y-3})=\\ \\=(\frac{3y^2+2y-3}{(y+2)^2}- \frac{5y+4}{y+2}* \frac{y+2}{y+2} )*( \frac{5y+2}{(y-3)(y+3)}+ \frac{y-6}{y-3}* \frac{y+3}{y+3})=\\=(\frac{3y^2+2y-3}{(y+2)^2}- \frac{(5y+4)(y+2)}{(y+2)^2} )*( \frac{5y+2}{(y-3)(y+3)}+ \frac{(y-6)(y+3)}{(y-3)(y+3)})=](https://tex.z-dn.net/?f=%28%5Cfrac%7B3y%5E2%2B2y-3%7D%7By%5E2%2B4y%2B4%7D-+%5Cfrac%7B5y%2B4%7D%7By%2B2%7D%29%2A%28+%5Cfrac%7B5y%2B2%7D%7By%5E2-9%7D%2B+%5Cfrac%7By-6%7D%7By-3%7D%29%3D%5C%5C+%5C%5C%3D%28%5Cfrac%7B3y%5E2%2B2y-3%7D%7B%28y%2B2%29%5E2%7D-+%5Cfrac%7B5y%2B4%7D%7By%2B2%7D%2A+%5Cfrac%7By%2B2%7D%7By%2B2%7D+%29%2A%28+%5Cfrac%7B5y%2B2%7D%7B%28y-3%29%28y%2B3%29%7D%2B+%5Cfrac%7By-6%7D%7By-3%7D%2A+%5Cfrac%7By%2B3%7D%7By%2B3%7D%29%3D%5C%5C%3D%28%5Cfrac%7B3y%5E2%2B2y-3%7D%7B%28y%2B2%29%5E2%7D-+%5Cfrac%7B%285y%2B4%29%28y%2B2%29%7D%7B%28y%2B2%29%5E2%7D+%29%2A%28+%5Cfrac%7B5y%2B2%7D%7B%28y-3%29%28y%2B3%29%7D%2B+%5Cfrac%7B%28y-6%29%28y%2B3%29%7D%7B%28y-3%29%28y%2B3%29%7D%29%3D)
![(\frac{3y^2+2y-3}{(y+2)^2}- \frac{(5y+4)(y+2)}{(y+2)^2} )*( \frac{5y+2}{(y-3)(y+3)}+ \frac{(y-6)(y+3)}{(y-3)(y+3)})= \\ \\ =(\frac{3y^2+2y-3}{(y+2)^2}- \frac{5y^2+4y+10y+8}{(y+2)^2} )*( \frac{5y+2}{(y-3)(y+3)}+ \frac{y^2+3y-6y-18}{(y-3)(y+3)})= \\ \\ =\frac{(3y^2+2y-3)-(5y^2+14y+8)}{(y+2)^2}* \frac{(5y+2)+(y^2-3y-18)}{(y-3)(y+3)}= \\ \\ =\frac{3y^2+2y-3-5y^2-14y-8}{(y+2)^2}* \frac{5y+2+y^2-3y-18}{(y-3)(y+3)}= (\frac{3y^2+2y-3}{(y+2)^2}- \frac{(5y+4)(y+2)}{(y+2)^2} )*( \frac{5y+2}{(y-3)(y+3)}+ \frac{(y-6)(y+3)}{(y-3)(y+3)})= \\ \\ =(\frac{3y^2+2y-3}{(y+2)^2}- \frac{5y^2+4y+10y+8}{(y+2)^2} )*( \frac{5y+2}{(y-3)(y+3)}+ \frac{y^2+3y-6y-18}{(y-3)(y+3)})= \\ \\ =\frac{(3y^2+2y-3)-(5y^2+14y+8)}{(y+2)^2}* \frac{(5y+2)+(y^2-3y-18)}{(y-3)(y+3)}= \\ \\ =\frac{3y^2+2y-3-5y^2-14y-8}{(y+2)^2}* \frac{5y+2+y^2-3y-18}{(y-3)(y+3)}=](https://tex.z-dn.net/?f=%28%5Cfrac%7B3y%5E2%2B2y-3%7D%7B%28y%2B2%29%5E2%7D-+%5Cfrac%7B%285y%2B4%29%28y%2B2%29%7D%7B%28y%2B2%29%5E2%7D+%29%2A%28+%5Cfrac%7B5y%2B2%7D%7B%28y-3%29%28y%2B3%29%7D%2B+%5Cfrac%7B%28y-6%29%28y%2B3%29%7D%7B%28y-3%29%28y%2B3%29%7D%29%3D+%5C%5C++%5C%5C+%3D%28%5Cfrac%7B3y%5E2%2B2y-3%7D%7B%28y%2B2%29%5E2%7D-+%5Cfrac%7B5y%5E2%2B4y%2B10y%2B8%7D%7B%28y%2B2%29%5E2%7D+%29%2A%28+%5Cfrac%7B5y%2B2%7D%7B%28y-3%29%28y%2B3%29%7D%2B+%5Cfrac%7By%5E2%2B3y-6y-18%7D%7B%28y-3%29%28y%2B3%29%7D%29%3D+%5C%5C++%5C%5C+%3D%5Cfrac%7B%283y%5E2%2B2y-3%29-%285y%5E2%2B14y%2B8%29%7D%7B%28y%2B2%29%5E2%7D%2A+%5Cfrac%7B%285y%2B2%29%2B%28y%5E2-3y-18%29%7D%7B%28y-3%29%28y%2B3%29%7D%3D+%5C%5C++%5C%5C+%3D%5Cfrac%7B3y%5E2%2B2y-3-5y%5E2-14y-8%7D%7B%28y%2B2%29%5E2%7D%2A+%5Cfrac%7B5y%2B2%2By%5E2-3y-18%7D%7B%28y-3%29%28y%2B3%29%7D%3D)
![\frac{-2y^2-12y-11}{(y+2)^2}* \frac{y^2+2y-16}{(y-3)(y+3)}=\frac{(-2y^2-12y-11)*(y^2+2y-16)}{(y+2)^2*(y-3)(y+3)}= \\ \\ =\frac{-2y^4-4y^3+32y^2-12y^3-24y^2+192y-11y^2-22y+176}{(y+2)^2*(y-3)(y+3)}= \\ \\ =\frac{-2y^4-16y^3-3y^2+192y+176}{(y+2)^2*(y-3)(y+3)} \frac{-2y^2-12y-11}{(y+2)^2}* \frac{y^2+2y-16}{(y-3)(y+3)}=\frac{(-2y^2-12y-11)*(y^2+2y-16)}{(y+2)^2*(y-3)(y+3)}= \\ \\ =\frac{-2y^4-4y^3+32y^2-12y^3-24y^2+192y-11y^2-22y+176}{(y+2)^2*(y-3)(y+3)}= \\ \\ =\frac{-2y^4-16y^3-3y^2+192y+176}{(y+2)^2*(y-3)(y+3)}](https://tex.z-dn.net/?f=%5Cfrac%7B-2y%5E2-12y-11%7D%7B%28y%2B2%29%5E2%7D%2A+%5Cfrac%7By%5E2%2B2y-16%7D%7B%28y-3%29%28y%2B3%29%7D%3D%5Cfrac%7B%28-2y%5E2-12y-11%29%2A%28y%5E2%2B2y-16%29%7D%7B%28y%2B2%29%5E2%2A%28y-3%29%28y%2B3%29%7D%3D+%5C%5C++%5C%5C+%3D%5Cfrac%7B-2y%5E4-4y%5E3%2B32y%5E2-12y%5E3-24y%5E2%2B192y-11y%5E2-22y%2B176%7D%7B%28y%2B2%29%5E2%2A%28y-3%29%28y%2B3%29%7D%3D+%5C%5C++%5C%5C+%3D%5Cfrac%7B-2y%5E4-16y%5E3-3y%5E2%2B192y%2B176%7D%7B%28y%2B2%29%5E2%2A%28y-3%29%28y%2B3%29%7D)
Esto es lo máximo que lo pude simplificar, seguramente haya algún error al escribir el enunciado. Si puedes revísalo y coloca paréntesis para definir cada numerados y cada denominador. Un saludo.
Esto es lo máximo que lo pude simplificar, seguramente haya algún error al escribir el enunciado. Si puedes revísalo y coloca paréntesis para definir cada numerados y cada denominador. Un saludo.
Respuesta dada por:
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Respuesta:
esta dificil
Explicación paso a paso:
no puesdo xd caca caca
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