Solve frac{u^{3}v-3u^{2}v^2}{3uv^3-u^2v^2}

$$\frac { u ^ { 3 } v - 3 u ^ { 2 } v ^ { 2 } } { 3 u v ^ { 3 } - u ^ { 2 } v ^ { 2 } }$$

Evaluate

$$-\frac{u}{v}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{v\left(u-3v\right)u^{2}}{u\left(-u+3v\right)v^{2}}$$

Extract the negative sign in u-3v.

$$\frac{-v\left(-u+3v\right)u^{2}}{u\left(-u+3v\right)v^{2}}$$

Cancel out uv\left(-u+3v\right) in both numerator and denominator.

$$\frac{-u}{v}$$

Expand

$$-\frac{u}{v}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{v\left(u-3v\right)u^{2}}{u\left(-u+3v\right)v^{2}}$$

Extract the negative sign in u-3v.

$$\frac{-v\left(-u+3v\right)u^{2}}{u\left(-u+3v\right)v^{2}}$$

Cancel out uv\left(-u+3v\right) in both numerator and denominator.

$$\frac{-u}{v}$$