Answer
$$\frac{(w-7)(w-8)}{(2w-7)(3w+1)}$$
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:
$$ \frac{\left(w^2-14w+49\right)}{2w^2-3w-14}\times \frac{w^2-6w-16}{\left(3w^2-20w-7\right)}\\ \frac{\left(w^2-14w+49\right)\left(w^2-6w-16\right)}{\left(2w^2-3w-14\right)\left(3w^2-20w-7\right)}\\ \frac{\left(w-7\right)\left(w-8\right)}{\left(2w-7\right)\left(3w+1\right)}\\ \frac{\left(w-7\right)\left(w-8\right)}{6w^2-19w-7}\\ \frac{w^2-15w+56}{6w^2-19w-7}\\ \frac{(w-7)(w-8)}{(2w-7)(3w+1)}$$
