Answer
$\frac{1}{q^2}$.
Work Step by Step
The given expression is
$=\frac{\frac{1}{q+4}}{\frac{2q^2}{2q+8}}$
Write as a quotient.
$=\frac{1}{q+4}\div \frac{2q^2}{2q+8}$
$=\frac{1}{q+4}\times \frac{2q+8}{2q^2}$
Factor.
$=\frac{1}{q+4}\times \frac{2(q+4)}{2q^2}$
Divide out the common factors.
$= \frac{1}{q^2}$.
