Answer
$12$
Work Step by Step
Dividing with $\displaystyle \frac{P}{Q}$ equals multiplying with the reciprocal, $\displaystyle \frac{Q}{P}.$
$\displaystyle \frac{9}{x}\div\frac{3}{4x}=\frac{9}{x}\cdot\frac{4x}{3}\qquad$... divide out the common factors
$=\displaystyle \frac{3}{1}\cdot\frac{4\cdot 1}{1}$
= $12$