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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. 329 (page 982)

In the following exercises, solve.
$\frac{x - 10}{x^{2} + 8 x + 12} = \frac{3}{x + 2} + \frac{4}{x + 6}$

Short Answer

Expert verified

The solution is $x = - 6 .$

Step by step solution

01

Step 1. Given Information

The given rational expression is

$\frac{x - 10}{x^{2} + 8 x + 12} = \frac{3}{x + 2} + \frac{4}{x + 6}$

02

Step 2. Removing the fraction

The Least common denominator is

$(x + 2) (x + 6)$

Multiply the equation by the LCD,

$(x + 2) (x + 6) 脳 \frac{x - 10}{x^{2} + 8 x + 12} = [\frac{3}{x + 2} + \frac{4}{x + 6}] (x + 2) (x + 6) x^{2} + 8 x + 12 脳 \frac{x - 10}{x^{2} + 8 x + 12} = 3 (x + 6) + 4 (x + 2) x - 10 = 3 x + 18 + 4 x + 8 x - 10 = 7 x + 26 - 6 x = 36 x = - 6$

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