Solve 1/frac{1{b}+1/a}

$$\frac { 1 } { \frac { 1 } { b } + \frac { 1 } { a } }$$

Evaluate

$$\frac{ab}{a+b}$$

Solution Steps

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

$$\frac{1}{\frac{a}{ab}+\frac{b}{ab}}$$

Since \frac{a}{ab} and \frac{b}{ab} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{a+b}{ab}}$$

Divide 1 by \frac{a+b}{ab} by multiplying 1 by the reciprocal of \frac{a+b}{ab}.

$$\frac{ab}{a+b}$$

Factor

$$\frac{ab}{a+b}$$