Question

Solve for $x$ :
$\frac{1}{(x-3)}-\frac{1}{(x+5)}=\frac{1}{6}x\ne 3$ and $x\ne -5$

Answer 1

Given,

$\frac{1}{x-3}-\frac{1}{x+5}=\frac{1}{6}$

$6(x+5)-6(x-3)=(x-3)(x+5)$

$6x+30-6x+18=x^2+2x-15$

$48=x^2+2x-15$

$x^2+2x-63=0$

$(x-7)(x+9)=0$

$\therefore x=-9,7$