Answer
$$\frac{3x}{10}$$
Work Step by Step
Recall, one never divides by a fraction. Rather, if we want to divide by a fraction, we multiply by the reciprocal of the fraction. Recall, the reciprocal of a fraction is that fraction with the numerator and the denominator switched. Thus, we find:
$$ \frac{3}{5x}\times \frac{x^2}{2}\\ \frac{3x^2}{10x}\\ \frac{3x}{10}$$