Question

Solve:

$\frac{1}{x-1}-\frac{1}{x+5}=\frac{6}{7},x\ne 1,-5$

Answer 1

$\frac{1}{x-1}-\frac{1}{x+5}=\frac{6}{7}$

$\Rightarrow \frac{x+5-(x-1)}{(x-1)(x+5)}=\frac{6}{7}$

$\Rightarrow \frac{6}{(x-1)(x+5)}=\frac{6}{7}$

$\Rightarrow 7=(x-1)(x+5)$

$\Rightarrow x^2+4x-5=7$

$\Rightarrow x^2+4x-12=0$

$\Rightarrow x^2+6x-2x-12=0$

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

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

$\Rightarrow x=-6$ or $x=2$

$\therefore$ roots are $2,-6$.