Solve frac{m^{-3}-n^{-1}m^-1}{n^-1m^-2-n^-2}

$$\frac { m ^ { - 3 } - n ^ { - 1 } m ^ { - 1 } } { n ^ { - 1 } m ^ { - 2 } - n ^ { - 2 } }$$

Evaluate

$$\frac{n}{m}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{m^{-2}\times \frac{1}{m}\left(-\frac{1}{n}m^{2}+1\right)}{m^{-2}\times \frac{1}{n}\left(-\frac{1}{n}m^{2}+1\right)}$$

Cancel out m^{-2}\left(-\frac{1}{n}m^{2}+1\right) in both numerator and denominator.

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

Divide \frac{1}{m} by \frac{1}{n} by multiplying \frac{1}{m} by the reciprocal of \frac{1}{n}.

$$\frac{n}{m}$$

Expand

$$\frac{n}{m}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{m^{-2}\times \frac{1}{m}\left(-\frac{1}{n}m^{2}+1\right)}{m^{-2}\times \frac{1}{n}\left(-\frac{1}{n}m^{2}+1\right)}$$

Cancel out m^{-2}\left(-\frac{1}{n}m^{2}+1\right) in both numerator and denominator.

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

Divide \frac{1}{m} by \frac{1}{n} by multiplying \frac{1}{m} by the reciprocal of \frac{1}{n}.

$$\frac{n}{m}$$