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