Answer
$\displaystyle \frac{3(x-4)}{5x}$
Work Step by Step
$...=\displaystyle \frac{12x}{5x+20}\div\frac{4x^{2}}{x^{2}-16}=\frac{12x}{5x+20}\cdot\frac{x^{2}-16}{4x^{2}}$
Factoring,
$12=4\cdot 3$
$ x^{2}-16=(x+4)(x-4)\quad$ (a difference of squares)
$5x+20=5(x+4)$
$x^{2}=x\cdot x$
... = $\displaystyle \frac{4\cdot 3\cdot x\cdot(x+4)(x-4)}{5(x+4)\cdot 4\cdot x\cdot x}$
... cancel the following from both sides of the fraction line:
$4,\ x$, $(x+4)$
... = $\displaystyle \frac{3(x-4)}{5x}$
