Solve frac{80m^{2}n^{3}k^{2}-20m^{4}nk^{2}}{16m^{3}nk^{2}-64m^{2}n^2k^2+64mn^3k^2}

$$\frac { 80 m ^ { 2 } n ^ { 3 } k ^ { 2 } - 20 m ^ { 4 } n k ^ { 2 } } { 16 m ^ { 3 } n k ^ { 2 } - 64 m ^ { 2 } n ^ { 2 } k ^ { 2 } + 64 m n ^ { 3 } k ^ { 2 } }$$

Evaluate

$$\frac{5m\left(m+2n\right)}{4\left(2n-m\right)}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{20n\left(m+2n\right)\left(-m+2n\right)k^{2}m^{2}}{16mnk^{2}\left(m-2n\right)^{2}}$$

Cancel out 4mnk^{2} in both numerator and denominator.

$$\frac{5m\left(m+2n\right)\left(-m+2n\right)}{4\left(m-2n\right)^{2}}$$

Expand the expression.

$$\frac{-5m^{3}+20mn^{2}}{4m^{2}-16mn+16n^{2}}$$

Factor the expressions that are not already factored.

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

Cancel out m-2n in both numerator and denominator.

$$\frac{5m\left(-m-2n\right)}{4\left(m-2n\right)}$$

Expand the expression.

$$\frac{-5m^{2}-10mn}{4m-8n}$$

Expand

$$\frac{5\left(m^{2}+2mn\right)}{4\left(2n-m\right)}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{20n\left(m+2n\right)\left(-m+2n\right)k^{2}m^{2}}{16mnk^{2}\left(m-2n\right)^{2}}$$

Cancel out 4mnk^{2} in both numerator and denominator.

$$\frac{5m\left(m+2n\right)\left(-m+2n\right)}{4\left(m-2n\right)^{2}}$$

Expand the expression.

$$\frac{-5m^{3}+20mn^{2}}{4m^{2}-16mn+16n^{2}}$$

Factor the expressions that are not already factored.

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

Cancel out m-2n in both numerator and denominator.

$$\frac{5m\left(-m-2n\right)}{4\left(m-2n\right)}$$

Expand the expression.

$$\frac{-5m^{2}-10mn}{4m-8n}$$