Q. 7.8 - Intermediate Algebra

Question

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

Step-by-Step Solution

Answer

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

Step 1 . Given information

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

Step 2 . Simplify

$$\begin{gathered} \frac{x^2+x-2}{1-x^2}=\frac{(x-1)(x+2)}{(1-x)(1+x)} \text{Factorize numerator and denominator} \\ =-\frac{(x-1)(x+2)}{(x-1)(x+1)} \text{Rewrite the expression} \\ =-\frac{(x+2)}{(x+1)} \text{ Remove all the common factors } \end{gathered}$$

Hence, $-\frac{(x+2)}{(x+1)}$.