Question

Solve for $x$ :
$2\left(\frac{x-1}{x+3}\right)-7\left(\frac{x+3}{x-1}\right)=5,x\ne -3,1$

Answer 1

$2\left(\frac{x-1}{x+3}\right)-7\left(\frac{x+3}{x-1}\right)=5$

$\Rightarrow \frac{2{(x-1)}^2-7{(x+3)}^2}{(x+3)(x-1)}=5$

$\Rightarrow 2x^2+2-4x-7x^2-63-42x=5x^2+10x-15$

$\Rightarrow 10x^2+56x+46=0$

$\Rightarrow 5x^2+28x+23=0$

$\Rightarrow 5x^2+5x+23x+23=0$

$\Rightarrow (x+1)(5x+23)=0$

$\Rightarrow x=-1$ OR $x=-\frac{23}{5}$