Solve 1/p+1/q/frac{p+q{pq}}=

$$\frac { \frac { 1 } { p } + \frac { 1 } { q } } { \frac { p + q } { p q } } =$$

Evaluate

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Solution Steps

Divide \frac{1}{p}+\frac{1}{q} by \frac{p+q}{pq} by multiplying \frac{1}{p}+\frac{1}{q} by the reciprocal of \frac{p+q}{pq}.

$$\frac{\left(\frac{1}{p}+\frac{1}{q}\right)pq}{p+q}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of p and q is pq. Multiply \frac{1}{p} times \frac{q}{q}. Multiply \frac{1}{q} times \frac{p}{p}.

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

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

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

Express \frac{q+p}{pq}p as a single fraction.

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

Cancel out p in both numerator and denominator.

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

Cancel out q and q.

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

Cancel out p+q in both numerator and denominator.

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Factor

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