Solve m-n/ndiv(m^2+n^2/m-2n)

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply -2n times \frac{m}{m}.

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

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

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

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

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

Factor the expressions that are not already factored.

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

Cancel out m-n in both numerator and denominator.

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

Expand the expression.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply -2n times \frac{m}{m}.

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

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

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

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

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

Factor the expressions that are not already factored.

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

Cancel out m-n in both numerator and denominator.

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

Expand the expression.

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