Multiply and Divide Rational Expressions: example 8.26

$\begin{array}{cccc}& & & \hfill \frac{p^3+q^3}{2p^2+2pq+2q^2}÷\frac{p^2-q^2}{6}\hfill \\ \\ \\ \begin{array}{c}\text{Rewrite the division as a multiplication}\hfill \\ \text{of the first expression times the}\hfill \\ \text{reciprocal of the second.}\hfill \end{array}\hfill & & & \hfill \frac{p^3+q^3}{2p^2+2pq+2q^2}·\frac{6}{p^2-q^2}\hfill \\ \\ \\ \begin{array}{c}\text{Factor the numerators and denominators}\hfill \\ \text{and then multiply.}\hfill \end{array}\hfill & & & \hfill \frac{\left(p+q\right)\left(p^2-pq+q^2\right)6}{2\left(p^2+pq+q^2\right)\left(p-q\right)\left(p+q\right)}\hfill \\ \\ \\ \text{Simplify by dividing out common factors.}\hfill & & & \hfill \frac{\cancel{\left(p+q\right)}\left(p^2-pq+q^2\right){\cancel{6}}^3}{\cancel{2}\left(p^2+pq+q^2\right)\left(p-q\right)\cancel{\left(p+q\right)}}\hfill \\ \\ \\ \text{Simplify.}\hfill & & & \hfill \frac{3\left(p^2-pq+q^2\right)}{\left(p-q\right)\left(p^2+pq+q^2\right)}\hfill \end{array}$