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

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

Evaluate

$$n-m$$

Solution Steps

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

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

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

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

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

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

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

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

Cancel out m in both numerator and denominator.

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

Cancel out n and n.

$$-m+n$$

Expand

$$n-m$$

Solution Steps

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

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

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

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

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

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

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

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

Cancel out m in both numerator and denominator.

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

Cancel out n and n.

$$-m+n$$