Question

Simplify$\frac{x^2+x-2}{1-x^2}.$

Short answer

The simplest form of the given expression is$-\frac{(x+2)}{(x+1)}.$

Step-by-step solution

Step 1. Given information

The given expression is$\frac{x^2+x-2}{1-x^2}$

Step 2. Simplify

$$\begin{gathered} \frac{x^2+x-2}{1-x^2}=\frac{(x-1)(x+2)}{(1-x)(1+x)}\text{Factorizenumeratoranddenominator} \\ =-\frac{(x-1)(x+2)}{(x-1)(x+1)}\text{Rewritetheexpression} \\ =-\frac{(x+2)}{(x+1)}\text{Removeallthecommonfactors} \end{gathered}$$

Hence,$-\frac{(x+2)}{(x+1)}$.