Answer
$\frac{p^3-16p+3}{p+4}$
Work Step by Step
Step 1. Perform operations to the numerator:
$\frac{3}{p^2-16}+p=\frac{3+p^3-16p}{p^2-16}=\frac{p^3-16p+3}{(p+4)(p-4)}$
Step 2. Use the above result in the original expression, we have:
$\frac{\frac{3}{p^2-16}+p}{\frac{1}{p-4}}=\frac{\frac{p^3-16p+3}{(p+4)(p-4)}}{\frac{1}{p-4}}=\frac{p^3-16p+3}{(p+4)(p-4)}\cdot\frac{p-4}{1}=\frac{p^3-16p+3}{p+4}$
