Answer
$$\frac{2a}{3\left(a+3\right)}$$
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:
$$ \frac{10}{a+3}\div \frac{15}{a}\\ \frac{10}{a+3}\times \frac{a}{15}\\ \frac{10a}{\left(a+3\right)\times \:15}\\ \frac{2a}{3\left(a+3\right)}$$