Solve frac{m^{2}-4n^{2}}{mn(m+2n)}divm^2-4mn+4n^2/m^2n^2

$$\frac { m ^ { 2 } - 4 n ^ { 2 } } { m n ( m + 2 n ) } \div \frac { m ^ { 2 } - 4 m n + 4 n ^ { 2 } } { m ^ { 2 } n ^ { 2 } }$$

Evaluate

$$\frac{mn}{m-2n}$$

Short Solution Steps

Divide \frac{m^{2}-4n^{2}}{mn\left(m+2n\right)} by \frac{m^{2}-4mn+4n^{2}}{m^{2}n^{2}} by multiplying \frac{m^{2}-4n^{2}}{mn\left(m+2n\right)} by the reciprocal of \frac{m^{2}-4mn+4n^{2}}{m^{2}n^{2}}.

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

Cancel out mn in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out \left(m-2n\right)\left(m+2n\right) in both numerator and denominator.

$$\frac{mn}{m-2n}$$

Expand

$$-\frac{mn}{2n-m}$$

Short Solution Steps

Divide \frac{m^{2}-4n^{2}}{mn\left(m+2n\right)} by \frac{m^{2}-4mn+4n^{2}}{m^{2}n^{2}} by multiplying \frac{m^{2}-4n^{2}}{mn\left(m+2n\right)} by the reciprocal of \frac{m^{2}-4mn+4n^{2}}{m^{2}n^{2}}.

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

Cancel out mn in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out \left(m-2n\right)\left(m+2n\right) in both numerator and denominator.

$$\frac{mn}{m-2n}$$