Solve frac{u^{2}-v^{2}}{u^3-v^3}divu+v/u^2+uv+v^2

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

Evaluate

$$1$$

Short Solution Steps

Divide \frac{u^{2}-v^{2}}{u^{3}-v^{3}} by \frac{u+v}{u^{2}+uv+v^{2}} by multiplying \frac{u^{2}-v^{2}}{u^{3}-v^{3}} by the reciprocal of \frac{u+v}{u^{2}+uv+v^{2}}.

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

Factor the expressions that are not already factored.

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

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

$$1$$

Factor

$$1$$