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