Answer
$\displaystyle \frac{4x}{(x-2)(x-3)}$
Work Step by Step
$...=\displaystyle \frac{6x}{x^{2}-4}\div\frac{3x-9}{2x+4}=\frac{6x}{x^{2}-4}\cdot\frac{2x+4}{3x-9}$
Factoring,
$6=2\cdot 3$
$ x^{2}-4=(x+2)(x-2)\quad$ (a difference of squares)
$2x+4=2(x+2)$
$3x-9=3(x-3)$
... = $\displaystyle \frac{2\cdot 3\cdot x\cdot 2(x+2)}{(x+2)(x-2)\cdot 3(x-3)}$
... cancel the following from both sides of the fraction line:
$3$, $(x+2)$
... = $\displaystyle \frac{4x}{(x-2)(x-3)}$
