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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 8: Q 68. (page 919)

In the following exercises, simplify each rational expression.
$\frac{b^{2} + b - 42}{36 - b^{2}}$

Short Answer

Expert verified

The result is $- \frac{(b + 7)}{(6 + b)}$ .

Step by step solution

01

Step 1. Given information.

Consider the given information.

$\frac{b^{2} + b - 42}{36 - b^{2}}$

02

Step 2. Factor the fraction.

Factor the numerator and denominator of the given fraction and remove common factors.

$\begin{array}{l} \frac{b^{2} + b - 42}{36 - b^{2}} = \frac{b^{2} + 7 b - 6 b - 42}{6^{2} - b^{2}} \\ = \frac{b (b + 7) - 6 (b + 7)}{(6 - b) (6 + b)} \\ = \frac{(b - 6) (b + 7)}{(6 - b) (6 + b)} \\ = \frac{- (6 - b) (b + 7)}{(6 - b) (6 + b)} \\ = - \frac{(b + 7)}{(6 + b)} \end{array}$

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Most popular questions from this chapter

Heart Rate At the gym, Carol takes her pulse for 10 seconds and counts 19 beats.

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Simplify

In the following exercises, use either method.

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$\frac{\frac{1}{2} - \frac{1}{6}}{\frac{2}{3} + \frac{3}{4}}$

Solve :

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