Solve 18w^4/frac{4v^2-4u^2{9uw-9vw}}

$$\frac { 18 w ^ { 4 } } { \frac { 4 v ^ { 2 } - 4 u ^ { 2 } } { 9 u w - 9 v w } }$$

Evaluate

$$-\frac{81w^{5}}{2\left(u+v\right)}$$

Short Solution Steps

Divide 18w^{4} by \frac{4v^{2}-4u^{2}}{9uw-9vw} by multiplying 18w^{4} by the reciprocal of \frac{4v^{2}-4u^{2}}{9uw-9vw}.

$$\frac{18w^{4}\left(9uw-9vw\right)}{4v^{2}-4u^{2}}$$

Factor the expressions that are not already factored.

$$\frac{9\times 18w\left(u-v\right)w^{4}}{4\left(u+v\right)\left(-u+v\right)}$$

Extract the negative sign in u-v.

$$\frac{-9\times 18w\left(-u+v\right)w^{4}}{4\left(u+v\right)\left(-u+v\right)}$$

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

$$\frac{-9\times 9ww^{4}}{2\left(u+v\right)}$$

Expand the expression.

$$\frac{-81w^{5}}{2u+2v}$$

Expand

$$-\frac{81w^{5}}{2\left(u+v\right)}$$

Short Solution Steps

Divide 18w^{4} by \frac{4v^{2}-4u^{2}}{9uw-9vw} by multiplying 18w^{4} by the reciprocal of \frac{4v^{2}-4u^{2}}{9uw-9vw}.

$$\frac{18w^{4}\left(9uw-9vw\right)}{4v^{2}-4u^{2}}$$

Factor the expressions that are not already factored.

$$\frac{9\times 18w\left(u-v\right)w^{4}}{4\left(u+v\right)\left(-u+v\right)}$$

Extract the negative sign in u-v.

$$\frac{-9\times 18w\left(-u+v\right)w^{4}}{4\left(u+v\right)\left(-u+v\right)}$$

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

$$\frac{-9\times 9ww^{4}}{2\left(u+v\right)}$$

Expand the expression.

$$\frac{-81w^{5}}{2u+2v}$$