Solve (2/n-1/n)div(m^2+n^2/n-5n)

$$( \frac { 2 } { n } - \frac { 1 } { n } ) \div ( \frac { m ^ { 2 } + n ^ { 2 } } { n } - 5 n )$$

Evaluate

$$\frac{1}{m^{2}-4n^{2}}$$

Short Solution Steps

Since \frac{2}{n} and \frac{1}{n} have the same denominator, subtract them by subtracting their numerators. Subtract 1 from 2 to get 1.

$$\frac{\frac{1}{n}}{\frac{m^{2}+n^{2}}{n}-5n}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -5n times \frac{n}{n}.

$$\frac{\frac{1}{n}}{\frac{m^{2}+n^{2}}{n}+\frac{-5nn}{n}}$$

Since \frac{m^{2}+n^{2}}{n} and \frac{-5nn}{n} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{n}}{\frac{m^{2}+n^{2}-5nn}{n}}$$

Do the multiplications in m^{2}+n^{2}-5nn.

$$\frac{\frac{1}{n}}{\frac{m^{2}+n^{2}-5n^{2}}{n}}$$

Combine like terms in m^{2}+n^{2}-5n^{2}.

$$\frac{\frac{1}{n}}{\frac{m^{2}-4n^{2}}{n}}$$

Divide \frac{1}{n} by \frac{m^{2}-4n^{2}}{n} by multiplying \frac{1}{n} by the reciprocal of \frac{m^{2}-4n^{2}}{n}.

$$\frac{n}{n\left(m^{2}-4n^{2}\right)}$$

Cancel out n in both numerator and denominator.

$$\frac{1}{m^{2}-4n^{2}}$$

Expand

$$\frac{1}{m^{2}-4n^{2}}$$

Short Solution Steps

Since \frac{2}{n} and \frac{1}{n} have the same denominator, subtract them by subtracting their numerators. Subtract 1 from 2 to get 1.

$$\frac{\frac{1}{n}}{\frac{m^{2}+n^{2}}{n}-5n}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -5n times \frac{n}{n}.

$$\frac{\frac{1}{n}}{\frac{m^{2}+n^{2}}{n}+\frac{-5nn}{n}}$$

Since \frac{m^{2}+n^{2}}{n} and \frac{-5nn}{n} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{n}}{\frac{m^{2}+n^{2}-5nn}{n}}$$

Do the multiplications in m^{2}+n^{2}-5nn.

$$\frac{\frac{1}{n}}{\frac{m^{2}+n^{2}-5n^{2}}{n}}$$

Combine like terms in m^{2}+n^{2}-5n^{2}.

$$\frac{\frac{1}{n}}{\frac{m^{2}-4n^{2}}{n}}$$

Divide \frac{1}{n} by \frac{m^{2}-4n^{2}}{n} by multiplying \frac{1}{n} by the reciprocal of \frac{m^{2}-4n^{2}}{n}.

$$\frac{n}{n\left(m^{2}-4n^{2}\right)}$$

Cancel out n in both numerator and denominator.

$$\frac{1}{m^{2}-4n^{2}}$$