Solve p^2-q^2/2p^3qdiv3p-3q/pq^2

$$\frac { p ^ { 2 } - q ^ { 2 } } { 2 p ^ { 3 } q } \div \frac { 3 p - 3 q } { p q ^ { 2 } }$$

Evaluate

$$\frac{q\left(p+q\right)}{6p^{2}}$$

Short Solution Steps

Divide \frac{p^{2}-q^{2}}{2p^{3}q} by \frac{3p-3q}{pq^{2}} by multiplying \frac{p^{2}-q^{2}}{2p^{3}q} by the reciprocal of \frac{3p-3q}{pq^{2}}.

$$\frac{\left(p^{2}-q^{2}\right)pq^{2}}{2p^{3}q\left(3p-3q\right)}$$

Cancel out pq in both numerator and denominator.

$$\frac{q\left(p^{2}-q^{2}\right)}{2\left(3p-3q\right)p^{2}}$$

Factor the expressions that are not already factored.

$$\frac{q\left(p+q\right)\left(p-q\right)}{2\times 3\left(p-q\right)p^{2}}$$

Cancel out p-q in both numerator and denominator.

$$\frac{q\left(p+q\right)}{2\times 3p^{2}}$$

Expand the expression.

$$\frac{pq+q^{2}}{6p^{2}}$$

Expand

$$\frac{pq+q^{2}}{6p^{2}}$$

Short Solution Steps

Divide \frac{p^{2}-q^{2}}{2p^{3}q} by \frac{3p-3q}{pq^{2}} by multiplying \frac{p^{2}-q^{2}}{2p^{3}q} by the reciprocal of \frac{3p-3q}{pq^{2}}.

$$\frac{\left(p^{2}-q^{2}\right)pq^{2}}{2p^{3}q\left(3p-3q\right)}$$

Cancel out pq in both numerator and denominator.

$$\frac{q\left(p^{2}-q^{2}\right)}{2\left(3p-3q\right)p^{2}}$$

Factor the expressions that are not already factored.

$$\frac{q\left(p+q\right)\left(p-q\right)}{2\times 3\left(p-q\right)p^{2}}$$

Cancel out p-q in both numerator and denominator.

$$\frac{q\left(p+q\right)}{2\times 3p^{2}}$$

Expand the expression.

$$\frac{pq+q^{2}}{6p^{2}}$$