Answer
$x=-17/5$
Work Step by Step
$\frac{4x}{(x^2+x-30)}+\frac{2}{(x-5)}=\frac{1}{(x+6)}$
$((x-5)(x+6))*(\frac{4x}{(x^2+x-30)}+\frac{2}{(x-5)})=((x-5)(x+6))*\frac{1}{(x+6)}$
$((x-5)(x+6))*(\frac{4x}{(x-5)(x+6)}+\frac{2}{(x-5)})=((x-5)(x+6))*\frac{1}{(x+6)}$
$(\frac{4x*(x-5)(x+6)}{(x-5)(x+6)}+\frac{2*(x-5)(x+6)}{(x-5)})=\frac{(x-5)(x+6)}{(x+6)}$
$4x+2*(x+6)=(x-5)$
$4x+2x+12=x-5$
$6x+12=x-5$
$5x+12=-5$
$5x+17=0$
$5x=-17$
$5x/5=-17/5$
$x=-17/5$
