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

Step 1. Given information.

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

Step 2. Solve using LCD.

We have

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

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve using LCD.

One App. One Place for Learning.

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Solve :xx+4=32x2-16+5.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve using LCD.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Probability and Statistics

Discrete Mathematics

Decision Maths

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

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