Question

Hola me podrian ayudar con esto porfa ​

Answer 1

$\frac{2}{x^2-2x-8}-\frac{3}{x^2+8x+12}+\frac{1}{x^2+2a-24}$

FACTORIZAR

$=\frac{2}{\left(x+2\right)\left(x-4\right)}-\frac{3}{x^2+8x+12}+\frac{1}{x^2+2a-24}$

FACTORIZAR

$=\frac{2}{\left(x+2\right)\left(x-4\right)}-\frac{3}{\left(x+2\right)\left(x+6\right)}+\frac{1}{x^2+2a-24}$

MINIMO COMUN MUTIPLO DE (X+2)(X-4),(X+2)(X+6), 2 ELEVADO A 2+ 2a- 24: (X+2)(X-4)(X+6)(X ELEVADO A 2 + 2a-24)

$=\frac{2\left(x+6\right)\left(x^2+2a-24\right)}{\left(x+2\right)\left(x-4\right)\left(x+6\right)\left(x^2+2a-24\right)}-\frac{3\left(x-4\right)\left(x^2+2a-24\right)}{\left(x+2\right)\left(x+6\right)\left(x-4\right)\left(x^2+2a-24\right)}+\frac{\left(x+2\right)\left(x-4\right)\left(x+6\right)}{\left(x+2\right)\left(x-4\right)\left(x+6\right)\left(x^2+2a-24\right)}$

$\mathrm{Ya\:que\:los\:denominadores\:son\:iguales,\:combinar\:las\:fracciones}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}$

$=\frac{2\left(x+6\right)\left(x^2+2a-24\right)-3\left(x-4\right)\left(x^2+2a-24\right)+\left(x+2\right)\left(x-4\right)\left(x+6\right)}{\left(x+2\right)\left(x-4\right)\left(x+6\right)\left(x^2+2a-24\right)}$

RESPUESTA

$=\frac{28x^2+4x-2ax+48a-624}{\left(x+2\right)\left(x-4\right)\left(x+6\right)\left(x^2+2a-24\right)}$