Solve (n/m-m/n)*m/n-m

$$( \frac { n } { m } - \frac { m } { n } ) \cdot \frac { m } { n - m }$$

Evaluate

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

Short Solution Steps

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

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

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

$$\frac{nn-mm}{mn}\times \frac{m}{n-m}$$

Do the multiplications in nn-mm.

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

Multiply \frac{n^{2}-m^{2}}{mn} times \frac{m}{n-m} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out m in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out -m+n in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

$$\frac{nn-mm}{mn}\times \frac{m}{n-m}$$

Do the multiplications in nn-mm.

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

Multiply \frac{n^{2}-m^{2}}{mn} times \frac{m}{n-m} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out m in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out -m+n in both numerator and denominator.

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