Chapter 7: Q. 7.73 (page 688)

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

Short Answer

Expert verified

The solution is $x = 3$ .

Step by step solution

Step 1. Given.

The given equation is: $\frac{x}{x + 4} = \frac{32}{x^{2} - 16} + 5 .$

Step 2. To find

We have to solve the given equation.

Step 3. Calculation

LCD of the denominators is $(x + 4) (x - 4)$ . Multiply both sides by the LCD and then solve the linear equation. After that check if the solution works.

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

For $x = - 4$ ,

$\frac{x}{x + 4} = \frac{32}{x^{2} - 16} + 5 \frac{- 4}{- 4 + 4} = \frac{32}{{(- 4)}^{2} - 16} + 5 \frac{- 4}{0} = \frac{32}{16 - 16} + 5 \frac{- 4}{0} = \frac{32}{0} + 5$

For $x = - 4$ , denominators are 0. So it is not a solution.

For $x = 3$ ,

$\frac{x}{x + 4} = \frac{32}{x^{2} - 16} + 5 \frac{3}{3 + 4} = \frac{32}{3^{2} - 16} + 5 \frac{3}{7} = \frac{32}{9 - 16} + 5 \frac{3}{7} = \frac{32}{- 7} + 5 \frac{3}{7} = \frac{- 32}{7} + 5 \frac{3}{7} = \frac{- 32}{7} + \frac{35}{7} \frac{3}{7} = \frac{- 32 + 35}{7} \frac{3}{7} = \frac{3}{7}$

So, $x = 3$ is a solution.

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

Short Answer

Step by step solution

Step 1. Given.

Step 2. To find

Step 3. Calculation

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

Short Answer

Step by step solution

Step 1. Given.

Step 2. To find

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Geometry

Mechanics Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Calculus

Study anywhere. Anytime. Across all devices.

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