Solve (m/m^2-n^2-1/m+n)divn/n-m

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

Evaluate

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

Short Solution Steps

Factor m^{2}-n^{2}.

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

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

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

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

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

Do the multiplications in m-\left(m-n\right).

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

Combine like terms in m-m+n.

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

Divide \frac{n}{\left(m+n\right)\left(m-n\right)} by \frac{n}{n-m} by multiplying \frac{n}{\left(m+n\right)\left(m-n\right)} by the reciprocal of \frac{n}{n-m}.

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

Extract the negative sign in n-m.

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

Cancel out n\left(m-n\right) in both numerator and denominator.

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

Expand

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

Short Solution Steps

Factor m^{2}-n^{2}.

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

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

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

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

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

Do the multiplications in m-\left(m-n\right).

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

Combine like terms in m-m+n.

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

Divide \frac{n}{\left(m+n\right)\left(m-n\right)} by \frac{n}{n-m} by multiplying \frac{n}{\left(m+n\right)\left(m-n\right)} by the reciprocal of \frac{n}{n-m}.

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

Extract the negative sign in n-m.

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

Cancel out n\left(m-n\right) in both numerator and denominator.

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