Answer
$ \frac{2(2x^2+5x-2)}{(x-2)(x+2)(x+3)}$
Work Step by Step
$\frac{4x}{x^2-4}-\frac{2}{x^2+x-6}=\frac{4x}{(x+2)(x-2)}-\frac{2}{(x-2)(x+3)}=\frac{4x(x+3)-2(x+2)}{(x-2)(x+2)(x+3)}=\frac{4x^2+10x-4}{(x-2)(x+2)(x+3)}=\frac{2(2x^2+5x-2)}{(x-2)(x+2)(x+3)}$
