Answer
$\dfrac{4x}{(x-2)(x-3)} $
Work Step by Step
We apply Method 1 (A51), to treat the numerator and denominator of the complex rational expression separately. So, by factoring both the denominator and numerator of each rational function and cancelling the common factors, we have
$$
\frac{\frac{6x}{x^2-4}}{\frac{3x-9}{2x+4}}= \frac{\frac{6x}{(x+2)(x-2)}}{\frac{3(x-3)}{2(x+2)}} \\
=\frac{6x}{(x+2)(x-2)} \frac{2(x+2)}{3(x-3)}=\frac{4x}{(x-2)(x-3)}
.$$
