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

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

Evaluate

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

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{\eta }{m} times \frac{n}{n}. Multiply \frac{m}{n} times \frac{m}{m}.

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

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

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

Do the multiplications in \eta n-mm.

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

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

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

Cancel out m in both numerator and denominator.

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

Use the distributive property to multiply n by -m+n.

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

Expand

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

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{\eta }{m} times \frac{n}{n}. Multiply \frac{m}{n} times \frac{m}{m}.

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

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

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

Do the multiplications in \eta n-mm.

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

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

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

Cancel out m in both numerator and denominator.

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

Use the distributive property to multiply n by -m+n.

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