Solve =2u/a-1+4a/1-u

$$= \frac { 2 u } { a - 1 } + \frac { 4 a } { 1 - u }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a-1 and 1-u is \left(a-1\right)\left(-u+1\right). Multiply \frac{2u}{a-1} times \frac{-u+1}{-u+1}. Multiply \frac{4a}{1-u} times \frac{a-1}{a-1}.

$$\frac{2u\left(-u+1\right)}{\left(a-1\right)\left(-u+1\right)}+\frac{4a\left(a-1\right)}{\left(a-1\right)\left(-u+1\right)}$$

Since \frac{2u\left(-u+1\right)}{\left(a-1\right)\left(-u+1\right)} and \frac{4a\left(a-1\right)}{\left(a-1\right)\left(-u+1\right)} have the same denominator, add them by adding their numerators.

$$\frac{2u\left(-u+1\right)+4a\left(a-1\right)}{\left(a-1\right)\left(-u+1\right)}$$

Do the multiplications in 2u\left(-u+1\right)+4a\left(a-1\right).

$$\frac{-2u^{2}+2u+4a^{2}-4a}{\left(a-1\right)\left(-u+1\right)}$$

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

$$\frac{-2u^{2}+2u+4a^{2}-4a}{-au+u+a-1}$$

Factor

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