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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. 561 (page 1026)

In the following exercises, add.
$\frac{2 x}{x^{2} + 10 x + 24} + \frac{3 x}{x^{2} + 8 x + 16}$

Short Answer

Expert verified

The sum is $\frac{x (5 x + 26)}{{(x + 4)}^{2} (x + 6)}$ .

Step by step solution

01

Step 1. Given Information.

Given expression for addition is:

$\frac{x (5 x + 26)}{{(x + 4)}^{2} (x + 6)}$ .

02

Step 2. Calculation.

$C o n s i d e r, \frac{2 x}{x^{2} + 10 x + 24} + \frac{3 x}{x^{2} + 8 x + 16} = \frac{2 x}{x^{2} + 4 x + 6 x + 24} + \frac{3 x}{{(x + 4)}^{2}} = \frac{2 x}{(x + 4) (x + 6)} + \frac{3 x}{{(x + 4)}^{2}} T a k i n g L C M = \frac{2 x (x + 4) + 3 x (x + 6)}{{(x + 4)}^{2} (x + 6)} = \frac{x (5 x + 26)}{{(x + 4)}^{2} (x + 6)}$

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