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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 8.77 (page 944)

Rewrite as equivalent rational expressions with denominator $(x + 3) (x - 4) (x + 4)$ .
$\frac{2}{x^{2} - x - 12}, \frac{1}{x^{2} - 16}$

Short Answer

Expert verified

The simplification of the rational expression is $\frac{2 x + 8}{(x + 3) (x - 4) (x + 4)}, \frac{x + 3}{(x + 3) (x - 4) (x + 4)}$

Step by step solution

01

Given information

The given rational expression is $\frac{2}{x^{2} - x - 12}, \frac{1}{x^{2} - 16}$

02

The simplification of the expression

$\frac{2}{x^{2} - 4 x + 3 x - 12}, \frac{1}{(x - 4) (x + 4)} \frac{2}{x (x - 4) + 3 (x - 4)}, \frac{1}{(x - 4) (x + 4)} \frac{2}{(x + 3) (x - 4)}, \frac{1}{(x - 4) (x + 4)}$

The LCD of the expression is $(x + 4) (x - 4) (x + 3)$

Multiply each numerator by the same factor .

$\frac{2 (x + 4)}{(x + 3) (x - 4) (x + 4)}, \frac{1 (x + 3)}{(x - 4) (x + 4) (x + 3)} \frac{2 x + 8}{(x + 3) (x - 4) (x + 4)}, \frac{x + 3}{(x - 4) (x + 4) (x + 3)}$

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Most popular questions from this chapter

Simplify

In the following exercises, use either method.

$\frac{x - \frac{3 x}{x + 2}}{\frac{3}{x + 2} + \frac{3}{x - 2}}$ .

Solve Proportions

$\frac{2 p + 4}{8} = \frac{p + 18}{6}$

In the following exercises, solve

$\frac{a}{9} + \frac{a + 3}{3 a} = \frac{1}{a}$

. In this section, you learned to simplify the complex fraction $\frac{\frac{3}{x + 2}}{\frac{x}{x^{2} - 4}}$

two ways: rewriting it as a division problem multiplying the numerator and denominator by the LCD Which method do you prefer? Why?

Solve: $\frac{2 x + 15}{9} = \frac{7 x + 3}{15}$ .

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