Solve u/1+u+u/1-u^2

$$\frac { u } { 1 + u } + \frac { u } { 1 - u ^ { 2 } }$$

Evaluate

$$\frac{u\left(2-u\right)}{1-u^{2}}$$

Short Solution Steps

Factor 1-u^{2}.

$$\frac{u}{1+u}+\frac{u}{\left(u-1\right)\left(-u-1\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 1+u and \left(u-1\right)\left(-u-1\right) is \left(u-1\right)\left(u+1\right). Multiply \frac{u}{1+u} times \frac{u-1}{u-1}. Multiply \frac{u}{\left(u-1\right)\left(-u-1\right)} times \frac{-1}{-1}.

$$\frac{u\left(u-1\right)}{\left(u-1\right)\left(u+1\right)}+\frac{-u}{\left(u-1\right)\left(u+1\right)}$$

Since \frac{u\left(u-1\right)}{\left(u-1\right)\left(u+1\right)} and \frac{-u}{\left(u-1\right)\left(u+1\right)} have the same denominator, add them by adding their numerators.

$$\frac{u\left(u-1\right)-u}{\left(u-1\right)\left(u+1\right)}$$

Do the multiplications in u\left(u-1\right)-u.

$$\frac{u^{2}-u-u}{\left(u-1\right)\left(u+1\right)}$$

Combine like terms in u^{2}-u-u.

$$\frac{u^{2}-2u}{\left(u-1\right)\left(u+1\right)}$$

Expand \left(u-1\right)\left(u+1\right).

$$\frac{u^{2}-2u}{u^{2}-1}$$

Factor

$$\frac{u\left(2-u\right)}{1-u^{2}}$$