Solve (2/7mn^{3}-m^2n^2+1/6n^4)div(4/3n^2)

$$( \frac { 2 } { 7 } m n ^ { 3 } - m ^ { 2 } n ^ { 2 } + \frac { 1 } { 6 } n ^ { 4 } ) \div ( \frac { 4 } { 3 } n ^ { 2 } )$$

Evaluate

$$\frac{3mn}{14}+\frac{n^{2}}{8}-\frac{3m^{2}}{4}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\frac{1}{42}n^{2}\left(-42m^{2}+12mn+7n^{2}\right)}{\frac{4}{3}n^{2}}$$

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

$$\frac{\frac{1}{42}\left(-42m^{2}+12mn+7n^{2}\right)}{\frac{4}{3}}$$

Expand the expression.

$$\frac{-m^{2}+\frac{2}{7}mn+\frac{1}{6}n^{2}}{\frac{4}{3}}$$

Divide -m^{2}+\frac{2}{7}mn+\frac{1}{6}n^{2} by \frac{4}{3} by multiplying -m^{2}+\frac{2}{7}mn+\frac{1}{6}n^{2} by the reciprocal of \frac{4}{3}.

$$\frac{\left(-m^{2}+\frac{2}{7}mn+\frac{1}{6}n^{2}\right)\times 3}{4}$$

Use the distributive property to multiply -m^{2}+\frac{2}{7}mn+\frac{1}{6}n^{2} by 3.

$$\frac{-3m^{2}+\frac{6}{7}mn+\frac{1}{2}n^{2}}{4}$$

Expand

$$\frac{3mn}{14}+\frac{n^{2}}{8}-\frac{3m^{2}}{4}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\frac{1}{42}n^{2}\left(-42m^{2}+12mn+7n^{2}\right)}{\frac{4}{3}n^{2}}$$

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

$$\frac{\frac{1}{42}\left(-42m^{2}+12mn+7n^{2}\right)}{\frac{4}{3}}$$

Expand the expression.

$$\frac{-m^{2}+\frac{2}{7}mn+\frac{1}{6}n^{2}}{\frac{4}{3}}$$

Divide -m^{2}+\frac{2}{7}mn+\frac{1}{6}n^{2} by \frac{4}{3} by multiplying -m^{2}+\frac{2}{7}mn+\frac{1}{6}n^{2} by the reciprocal of \frac{4}{3}.

$$\frac{\left(-m^{2}+\frac{2}{7}mn+\frac{1}{6}n^{2}\right)\times 3}{4}$$

Use the distributive property to multiply -m^{2}+\frac{2}{7}mn+\frac{1}{6}n^{2} by 3.

$$\frac{-3m^{2}+\frac{6}{7}mn+\frac{1}{2}n^{2}}{4}$$