Answer
$$-\frac{a}{b}$$
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:
$$ \frac{a}{a-b}\times \frac{b-a}{b}\\ \frac{a\left(b-a\right)}{\left(a-b\right)b}\\ \frac{a\left(b-a\right)}{-b\left(b-a\right)}\\ -\frac{a}{b}$$
