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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. 3.131 (page 978)

Solve :
$\frac{x}{x + 4} = \frac{32}{x^{2} - 16} + 5$ .

Short Answer

Expert verified

$x = 3, - 4$ .

Step by step solution

01

Step 1. Given information.

To solve $\frac{x}{x + 4} = \frac{32}{x^{2} - 16} + 5$ .

02

Step 2. Solve using LCD.

We have

$\frac{x}{x + 4} = \frac{32}{x^{2} - 16} + 5 \frac{x}{x + 4} = \frac{32}{(x - 4) (x + 4)} + 5; x 鈮� 4, - 4$

Take LCD and multiply it to both sides.

$(x + 4) (x - 4) [\frac{x}{x + 4}] = [\frac{32}{(x - 4) (x + 4)} + 5] (x + 4) (x - 4) x (x - 4) = 32 + 5 (x + 4) (x - 4) x^{2} - 4 x = 32 + 5 (x^{2} - 16) x^{2} - 4 x = 32 + 5 x^{2} - 80 0 = 4 x^{2} + 4 x - 48 4 (x^{2} + x + 12) = 0 x^{2} + x + 12 = 0 x^{2} + 4 x - 3 x + 12 = 0 x (x + 4) - 3 (x + 4) = 0 (x + 4) (x - 3) = 0 x = - 4 o r x = 3$

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