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

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

Evaluate

$$-\frac{1}{8w^{3}}$$

Short Solution Steps

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

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

Factor the expressions that are not already factored.

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

Extract the negative sign in u-v.

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

Cancel out 9w\left(u+v\right)\left(-u+v\right) in both numerator and denominator.

$$\frac{-1}{2\times 4w^{3}}$$

Expand the expression.

$$\frac{-1}{8w^{3}}$$

Expand

$$-\frac{1}{8w^{3}}$$

Short Solution Steps

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

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

Factor the expressions that are not already factored.

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

Extract the negative sign in u-v.

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

Cancel out 9w\left(u+v\right)\left(-u+v\right) in both numerator and denominator.

$$\frac{-1}{2\times 4w^{3}}$$

Expand the expression.

$$\frac{-1}{8w^{3}}$$