Answer
$$\frac{1}{b^3\left(a-3b\right)}$$
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:
$$ \frac{3a^2-5ab-12b^2}{\left(3ab+4b^2\right)\left(3b^2-ab\right)^2}\\ \frac{\left(3a+4b\right)\left(a-3b\right)}{b^3\left(3b-a\right)^2\left(3a+4b\right)}\\ \frac{1}{b^3\left(a-3b\right)}$$
