Solve 1+m/n/n-frac{m^2{n}}=

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{n}{n}.

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

Since \frac{n}{n} and \frac{m}{n} have the same denominator, add them by adding their numerators.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply n times \frac{n}{n}.

$$\frac{\frac{n+m}{n}}{\frac{nn}{n}-\frac{m^{2}}{n}}$$

Since \frac{nn}{n} and \frac{m^{2}}{n} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{n+m}{n}}{\frac{nn-m^{2}}{n}}$$

Do the multiplications in nn-m^{2}.

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

Divide \frac{n+m}{n} by \frac{n^{2}-m^{2}}{n} by multiplying \frac{n+m}{n} by the reciprocal of \frac{n^{2}-m^{2}}{n}.

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

Cancel out n in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out m+n in both numerator and denominator.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{n}{n}.

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

Since \frac{n}{n} and \frac{m}{n} have the same denominator, add them by adding their numerators.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply n times \frac{n}{n}.

$$\frac{\frac{n+m}{n}}{\frac{nn}{n}-\frac{m^{2}}{n}}$$

Since \frac{nn}{n} and \frac{m^{2}}{n} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{n+m}{n}}{\frac{nn-m^{2}}{n}}$$

Do the multiplications in nn-m^{2}.

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

Divide \frac{n+m}{n} by \frac{n^{2}-m^{2}}{n} by multiplying \frac{n+m}{n} by the reciprocal of \frac{n^{2}-m^{2}}{n}.

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

Cancel out n in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out m+n in both numerator and denominator.

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