Answer
$$\frac{\left(a+7\right)\left(a+1\right)}{3a-7}$$
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:
$$ \frac{\left(a+7\right)\left(a^2+8a+7\right)}{3a^2+14a-49}\\ \frac{\left(a+7\right)^2\left(a+1\right)}{\left(3a-7\right)\left(a+7\right)}]\\ \frac{\left(a+7\right)\left(a+1\right)}{3a-7}$$
