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

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

Evaluate

$$ab$$

Solution Steps

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

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

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

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

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

$$\frac{\left(a+b\right)ab}{b+a}$$

Cancel out a+b in both numerator and denominator.

$$ab$$

Expand

$$ab$$

Solution Steps

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

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

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

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

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

$$\frac{\left(a+b\right)ab}{b+a}$$

Cancel out a+b in both numerator and denominator.

$$ab$$