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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 8.78 (page 944)

Rewrite as equivalent rational expressions with denominator
$(x + 3) (x + 5) (x + 6)$
$\frac{x}{x^{2} + 8 x + 15}, \frac{5}{x^{2} + 9 x + 18}$ .

Short Answer

Expert verified

The simplification of the expression is $\frac{x^{2} + 6 x}{(x + 3) (x + 5) (x + 6)}, \frac{5 x + 25}{(x + 3) (x + 5) (x + 6)}$

Step by step solution

01

Given information

The given rational expression is $\frac{x}{x^{2} + 8 x + 15}, \frac{5}{x^{2} + 9 x + 18}$ .

02

The simplification of the expression

$\frac{x}{x^{2} + 5 x + 3 x + 15}, \frac{5}{x^{2} + 9 x + 18}$

Factorize the denominator

role="math" localid="1648482456775" $\frac{x}{x^{2} + 5 x + 3 x + 15}, \frac{5}{x^{2} + 6 x + 3 x + 18} \frac{x}{x (x + 5) + 3 (x + 5)}, \frac{5}{x (x + 6) + 3 (x + 6)} \frac{x}{(x + 3) (x + 5)}, \frac{5}{(x + 3) (x + 6)}$

The LCD of the denominator $(x + 3) (x + 5) (x + 6)$ .

$\frac{x (x + 6)}{(x + 3) (x + 5) (x + 6)}, \frac{5 (x + 5)}{(x + 3) (x + 5) (x + 6)} S i m p l i f y t h e n u m e r a t o r \frac{x^{2} + 6 x}{(x + 3) (x + 5) (x + 6)}, \frac{5 x + 25}{(x + 3) (x + 5) (x + 6)}$

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