Solve u^2-v^2/(u+v)^2/frac{4u-4v{3(u+v)}}=

$$\frac { \frac { u ^ { 2 } - v ^ { 2 } } { ( u + v ) ^ { 2 } } } { \frac { 4 u - 4 v } { 3 ( u + v ) } } =$$

Evaluate

$$\frac{3}{4}=0.75$$

Short Solution Steps

Divide \frac{u^{2}-v^{2}}{\left(u+v\right)^{2}} by \frac{4u-4v}{3\left(u+v\right)} by multiplying \frac{u^{2}-v^{2}}{\left(u+v\right)^{2}} by the reciprocal of \frac{4u-4v}{3\left(u+v\right)}.

$$\frac{\left(u^{2}-v^{2}\right)\times 3\left(u+v\right)}{\left(u+v\right)^{2}\left(4u-4v\right)}$$

Cancel out u+v in both numerator and denominator.

$$\frac{3\left(u^{2}-v^{2}\right)}{\left(u+v\right)\left(4u-4v\right)}$$

Factor the expressions that are not already factored.

$$\frac{3\left(u+v\right)\left(u-v\right)}{4\left(u+v\right)\left(u-v\right)}$$

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

$$\frac{3}{4}$$

Factor

$$\frac{3}{2 ^ {2}} = 0.75$$