Question

Solve the following equation:
$\frac{2x-2}{x^2-36}-\frac{x-2}{x^2-6x}=\frac{x-1}{x^2+6x}$

Answer 1

$\frac{2x-2}{x^2-36}-\frac{x-2}{x^2-6x}=\frac{x-1}{x^2+6x}$

$\Rightarrow \frac{2x-2}{x^2-36}=\frac{x-1}{x(x+6)}+\frac{x-2}{x(x-6)}$

$\Rightarrow \frac{2x-2}{x^2-36}=\frac{(x-1)(x-6)+(x-2)(x+6)}{x(x^2-36)}$

$\Rightarrow \frac{2x-2}{x^2-36}=\frac{x^2-7x+6+x^{2}4x-12}{(x^2-36)}$

$\Rightarrow (2x^2-2x)(x^2-36)=(2x^2-3x-6)(x^2-36)$

$\Rightarrow (x^2-36)(2x^2-2x-2x^2+3x+6)=0$

$\Rightarrow (x^2-36)(x+6)=0$

$\Rightarrow x=\pm 6$