Solve 2/m+2/n/frac{m+n{mn}}=

$$\frac { \frac { 2 } { m } + \frac { 2 } { n } } { \frac { m + n } { m n } } =$$

Evaluate

$$2$$

Short Solution Steps

Divide \frac{2}{m}+\frac{2}{n} by \frac{m+n}{mn} by multiplying \frac{2}{m}+\frac{2}{n} by the reciprocal of \frac{m+n}{mn}.

$$\frac{\left(\frac{2}{m}+\frac{2}{n}\right)mn}{m+n}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m and n is mn. Multiply \frac{2}{m} times \frac{n}{n}. Multiply \frac{2}{n} times \frac{m}{m}.

$$\frac{\left(\frac{2n}{mn}+\frac{2m}{mn}\right)mn}{m+n}$$

Since \frac{2n}{mn} and \frac{2m}{mn} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2n+2m}{mn}mn}{m+n}$$

Express \frac{2n+2m}{mn}m as a single fraction.

$$\frac{\frac{\left(2n+2m\right)m}{mn}n}{m+n}$$

Cancel out m in both numerator and denominator.

$$\frac{\frac{2m+2n}{n}n}{m+n}$$

Cancel out n and n.

$$\frac{2m+2n}{m+n}$$

Factor the expressions that are not already factored.

$$\frac{2\left(m+n\right)}{m+n}$$

Cancel out m+n in both numerator and denominator.

$$2$$

Factor

$$2$$