Solve 1/a+1/b/a+b

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

Evaluate

$$\frac{1}{ab}$$

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}.

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

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

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

Express \frac{\frac{b+a}{ab}}{a+b} as a single fraction.

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

Cancel out a+b in both numerator and denominator.

$$\frac{1}{ab}$$

Expand

$$\frac{1}{ab}$$

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}.

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

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

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

Express \frac{\frac{b+a}{ab}}{a+b} as a single fraction.

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

Cancel out a+b in both numerator and denominator.

$$\frac{1}{ab}$$