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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 7.8 (page 644)

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

Short Answer

Expert verified

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

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

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

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Simplifyx2+x-21-x2.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify

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