Solve p/q+p/p-q

$$\frac { p } { q } + \frac { p } { p - q }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of q and p-q is q\left(p-q\right). Multiply \frac{p}{q} times \frac{p-q}{p-q}. Multiply \frac{p}{p-q} times \frac{q}{q}.

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

Since \frac{p\left(p-q\right)}{q\left(p-q\right)} and \frac{pq}{q\left(p-q\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in p\left(p-q\right)+pq.

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

Combine like terms in p^{2}-pq+pq.

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

Expand q\left(p-q\right).

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

Factor

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