Solve 1/m^2n+1/mn^2/frac{1{m^2n}-1/mn^2}

$$\frac { \frac { 1 } { m ^ { 2 } n } + \frac { 1 } { m n ^ { 2 } } } { \frac { 1 } { m ^ { 2 } n } - \frac { 1 } { m n ^ { 2 } } }$$

Evaluate

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

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m^{2}n and mn^{2} is m^{2}n^{2}. Multiply \frac{1}{m^{2}n} times \frac{n}{n}. Multiply \frac{1}{mn^{2}} times \frac{m}{m}.

$$\frac{\frac{n}{m^{2}n^{2}}+\frac{m}{m^{2}n^{2}}}{\frac{1}{m^{2}n}-\frac{1}{mn^{2}}}$$

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

$$\frac{\frac{n+m}{m^{2}n^{2}}}{\frac{1}{m^{2}n}-\frac{1}{mn^{2}}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m^{2}n and mn^{2} is m^{2}n^{2}. Multiply \frac{1}{m^{2}n} times \frac{n}{n}. Multiply \frac{1}{mn^{2}} times \frac{m}{m}.

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

Since \frac{n}{m^{2}n^{2}} and \frac{m}{m^{2}n^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Cancel out m^{2}n^{2} in both numerator and denominator.

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

Expand

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

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m^{2}n and mn^{2} is m^{2}n^{2}. Multiply \frac{1}{m^{2}n} times \frac{n}{n}. Multiply \frac{1}{mn^{2}} times \frac{m}{m}.

$$\frac{\frac{n}{m^{2}n^{2}}+\frac{m}{m^{2}n^{2}}}{\frac{1}{m^{2}n}-\frac{1}{mn^{2}}}$$

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

$$\frac{\frac{n+m}{m^{2}n^{2}}}{\frac{1}{m^{2}n}-\frac{1}{mn^{2}}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m^{2}n and mn^{2} is m^{2}n^{2}. Multiply \frac{1}{m^{2}n} times \frac{n}{n}. Multiply \frac{1}{mn^{2}} times \frac{m}{m}.

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

Since \frac{n}{m^{2}n^{2}} and \frac{m}{m^{2}n^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Cancel out m^{2}n^{2} in both numerator and denominator.

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