Solve frac{p^{2}-q^2}{p^2}*pq+q^2/(p+q)^2

$$\frac { p ^ { 2 } - q ^ { 2 } } { p ^ { 2 } } \cdot \frac { p q + q ^ { 2 } } { ( p + q ) ^ { 2 } }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{pq+q^{2}}{\left(p+q\right)^{2}}.

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

Cancel out p+q in both numerator and denominator.

$$\frac{p^{2}-q^{2}}{p^{2}}\times \frac{q}{p+q}$$

Multiply \frac{p^{2}-q^{2}}{p^{2}} times \frac{q}{p+q} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

Cancel out p+q in both numerator and denominator.

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

Expand the expression.

$$\frac{pq-q^{2}}{p^{2}}$$

Expand

$$\frac{pq-q^{2}}{p^{2}}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{pq+q^{2}}{\left(p+q\right)^{2}}.

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

Cancel out p+q in both numerator and denominator.

$$\frac{p^{2}-q^{2}}{p^{2}}\times \frac{q}{p+q}$$

Multiply \frac{p^{2}-q^{2}}{p^{2}} times \frac{q}{p+q} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

Cancel out p+q in both numerator and denominator.

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

Expand the expression.

$$\frac{pq-q^{2}}{p^{2}}$$