Solve frac{12m^{2}-4n}{3m^2-n}div10m^2n/5m^2n^2

$$\frac { 12 m ^ { 2 } - 4 n } { 3 m ^ { 2 } - n } \div \frac { 10 m ^ { 2 } n } { 5 m ^ { 2 } n ^ { 2 } }$$

Evaluate

$$2n$$

Short Solution Steps

Divide \frac{12m^{2}-4n}{3m^{2}-n} by \frac{10m^{2}n}{5m^{2}n^{2}} by multiplying \frac{12m^{2}-4n}{3m^{2}-n} by the reciprocal of \frac{10m^{2}n}{5m^{2}n^{2}}.

$$\frac{\left(12m^{2}-4n\right)\times 5m^{2}n^{2}}{\left(3m^{2}-n\right)\times 10m^{2}n}$$

Cancel out 5nm^{2} in both numerator and denominator.

$$\frac{n\left(12m^{2}-4n\right)}{2\left(3m^{2}-n\right)}$$

Factor the expressions that are not already factored.

$$\frac{4n\left(3m^{2}-n\right)}{2\left(3m^{2}-n\right)}$$

Cancel out 2\left(3m^{2}-n\right) in both numerator and denominator.

$$2n$$

Expand

$$2n$$

Short Solution Steps

Divide \frac{12m^{2}-4n}{3m^{2}-n} by \frac{10m^{2}n}{5m^{2}n^{2}} by multiplying \frac{12m^{2}-4n}{3m^{2}-n} by the reciprocal of \frac{10m^{2}n}{5m^{2}n^{2}}.

$$\frac{\left(12m^{2}-4n\right)\times 5m^{2}n^{2}}{\left(3m^{2}-n\right)\times 10m^{2}n}$$

Cancel out 5nm^{2} in both numerator and denominator.

$$\frac{n\left(12m^{2}-4n\right)}{2\left(3m^{2}-n\right)}$$

Factor the expressions that are not already factored.

$$\frac{4n\left(3m^{2}-n\right)}{2\left(3m^{2}-n\right)}$$

Cancel out 2\left(3m^{2}-n\right) in both numerator and denominator.

$$2n$$