Answer
$10$
Work Step by Step
Dividing with $\displaystyle \frac{P}{Q}$ equals multiplying with the reciprocal, $\displaystyle \frac{Q}{P}.$
$\displaystyle \frac{15}{x}\div\frac{3}{2x}=\frac{15}{x}\cdot\frac{2x}{3}\qquad$... divide out the common factors
$=\displaystyle \frac{5}{1}\cdot\frac{2\cdot 1}{1}$
= $10$