Solve 2/x-1+4/1-x^2

$$\frac{ 2 }{ x-1 } + \frac{ 4 }{ 1- { x }^{ 2 } }$$

Evaluate

$$\frac{2}{x+1}$$

Short Solution Steps

Factor 1-x^{2}.

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

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

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

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

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

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

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

Combine like terms in -2x-2+4.

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

Factor the expressions that are not already factored in \frac{-2x+2}{\left(x-1\right)\left(-x-1\right)}.

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

Extract the negative sign in 1-x.

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

Cancel out x-1 in both numerator and denominator.

$$\frac{-2}{-x-1}$$

Factor

$$\frac{2}{x+1}$$