Solve 3(u+v)/5(u-v)divu^2-v^2/10(u-v)

$$\frac { 3 ( u + v ) } { 5 ( u - v ) } \div \frac { u ^ { 2 } - v ^ { 2 } } { 10 ( u - v ) }$$

Evaluate

$$\frac{6}{u-v}$$

Short Solution Steps

Divide \frac{3\left(u+v\right)}{5\left(u-v\right)} by \frac{u^{2}-v^{2}}{10\left(u-v\right)} by multiplying \frac{3\left(u+v\right)}{5\left(u-v\right)} by the reciprocal of \frac{u^{2}-v^{2}}{10\left(u-v\right)}.

$$\frac{3\left(u+v\right)\times 10\left(u-v\right)}{5\left(u-v\right)\left(u^{2}-v^{2}\right)}$$

Cancel out 5\left(u-v\right) in both numerator and denominator.

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

Multiply 2 and 3 to get 6.

$$\frac{6\left(u+v\right)}{u^{2}-v^{2}}$$

Factor the expressions that are not already factored.

$$\frac{6\left(u+v\right)}{\left(u+v\right)\left(u-v\right)}$$

Cancel out u+v in both numerator and denominator.

$$\frac{6}{u-v}$$

Expand

$$\frac{6}{u-v}$$

Short Solution Steps

Divide \frac{3\left(u+v\right)}{5\left(u-v\right)} by \frac{u^{2}-v^{2}}{10\left(u-v\right)} by multiplying \frac{3\left(u+v\right)}{5\left(u-v\right)} by the reciprocal of \frac{u^{2}-v^{2}}{10\left(u-v\right)}.

$$\frac{3\left(u+v\right)\times 10\left(u-v\right)}{5\left(u-v\right)\left(u^{2}-v^{2}\right)}$$

Cancel out 5\left(u-v\right) in both numerator and denominator.

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

Multiply 2 and 3 to get 6.

$$\frac{6\left(u+v\right)}{u^{2}-v^{2}}$$

Factor the expressions that are not already factored.

$$\frac{6\left(u+v\right)}{\left(u+v\right)\left(u-v\right)}$$

Cancel out u+v in both numerator and denominator.

$$\frac{6}{u-v}$$