Answer
$\frac{p+6q}{p+q}$
Work Step by Step
Factor each part:
$p^{2}-36q^{2} = (p+6q)(p-6q)$
$p^{2}-12pq+36q^{2} = (p-6q)(p-6q)$
$p^{2}-5pq-6q^{2}=(p-6q)(p+q)$
$p^{2}+2pq+q^{2}=(p+q)(p+q)$
Now you have:
$\frac{ (p+6q)(p-6q)}{(p-6q)(p-6q)}\times\frac{(p-6q)(p+q)}{(p+q)(p+q)}$
Cancel and simplify
$$\frac{p+6q}{p+q}$$
