Answer
$$\frac{9\left(u-1\right)}{16}$$
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:
$$ \frac{\left(3u^2-3\right)}{4}\times \frac{3}{4u+4}\\ \frac{9\left(u+1\right)\left(u-1\right)}{4\left(4u+4\right)}\\ \frac{9\left(u+1\right)\left(u-1\right)}{16\left(u+1\right)}\\ \frac{9\left(u-1\right)}{16}$$
