Solve 1/n+1/m/frac{1{mn}}

$$\frac { \frac { 1 } { n } + \frac { 1 } { m } } { \frac { 1 } { m n } }$$

Evaluate

$$m+n$$

Solution Steps

Divide \frac{1}{n}+\frac{1}{m} by \frac{1}{mn} by multiplying \frac{1}{n}+\frac{1}{m} by the reciprocal of \frac{1}{mn}.

$$\left(\frac{1}{n}+\frac{1}{m}\right)mn$$

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

$$\left(\frac{m}{mn}+\frac{n}{mn}\right)mn$$

Since \frac{m}{mn} and \frac{n}{mn} have the same denominator, add them by adding their numerators.

$$\frac{m+n}{mn}mn$$

Express \frac{m+n}{mn}m as a single fraction.

$$\frac{\left(m+n\right)m}{mn}n$$

Cancel out m in both numerator and denominator.

$$\frac{m+n}{n}n$$

Cancel out n and n.

$$m+n$$

Expand

$$m+n$$

Solution Steps

Divide \frac{1}{n}+\frac{1}{m} by \frac{1}{mn} by multiplying \frac{1}{n}+\frac{1}{m} by the reciprocal of \frac{1}{mn}.

$$\left(\frac{1}{n}+\frac{1}{m}\right)mn$$

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

$$\left(\frac{m}{mn}+\frac{n}{mn}\right)mn$$

Since \frac{m}{mn} and \frac{n}{mn} have the same denominator, add them by adding their numerators.

$$\frac{m+n}{mn}mn$$

Express \frac{m+n}{mn}m as a single fraction.

$$\frac{\left(m+n\right)m}{mn}n$$

Cancel out m in both numerator and denominator.

$$\frac{m+n}{n}n$$

Cancel out n and n.

$$m+n$$