Solve (1/m-n-n/m^2-mn)*m/n-m

$$( \frac { 1 } { m - n } - \frac { n } { m ^ { 2 } - m n } ) \cdot \frac { m } { n - m }$$

Evaluate

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

Short Solution Steps

Factor m^{2}-mn.

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

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

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

Since \frac{m}{m\left(m-n\right)} and \frac{n}{m\left(m-n\right)} have the same denominator, subtract them by subtracting their numerators.

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

Cancel out m-n in both numerator and denominator.

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

Multiply \frac{1}{m} times \frac{m}{n-m} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out m in both numerator and denominator.

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

Expand

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

Short Solution Steps

Factor m^{2}-mn.

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

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

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

Since \frac{m}{m\left(m-n\right)} and \frac{n}{m\left(m-n\right)} have the same denominator, subtract them by subtracting their numerators.

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

Cancel out m-n in both numerator and denominator.

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

Multiply \frac{1}{m} times \frac{m}{n-m} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out m in both numerator and denominator.

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