Solve m/mn-n^2-1/m-n-1/n

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

Evaluate

$$0$$

Short Solution Steps

Factor mn-n^{2}.

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

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

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

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

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

Cancel out m-n in both numerator and denominator.

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

Since \frac{1}{n} and \frac{1}{n} have the same denominator, subtract them by subtracting their numerators. Subtract 1 from 1 to get 0.

$$\frac{0}{n}$$

Zero divided by any non-zero term gives zero.

$$0$$

Factor

$$0$$