Chapter 11: Q22. (page 731)

Find each sum or difference.
$\frac{5}{x^{2} - 2 x - 24} + \frac{x}{x - 6}$

Short Answer

Expert verified

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

Step by step solution

Step 1. Find LCD.

As $x^{2} - 2 x - 24 = (x + 4) (x - 6)$ the LCD $(x + 4) (x - 6)$

Step 2. Factor.

Factor $x^{2} - 2 x - 24$ .

$\frac{5}{x^{2} - 2 x - 24} + \frac{x}{x - 6} = \frac{5}{(x + 4) (x - 6)} + \frac{x}{x - 6}$

Step 3. Write using LCD.

Write $\frac{x}{x - 6}$ using LCD.

$\frac{5}{(x + 4) (x - 6)} + \frac{x (x + 4)}{(x - 6) (x + 4)}$

Step 4. Simplify.

Simplify the above-obtained expression.

$\frac{5 + x (x + 4)}{(x + 4) (x - 6)} = \frac{x^{2} + 4 x + 5}{(x + 4) (x - 6)}$

Therefore, the sum of the given expression is $\frac{x^{2} + 4 x + 5}{(x + 4) (x - 6)}$ .

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Find each sum or difference.
$\frac{5}{x^{2} - 2 x - 24} + \frac{x}{x - 6}$

Short Answer

Step by step solution

Step 1. Find LCD.

Step 2. Factor.

Step 3. Write using LCD.

Step 4. Simplify.

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Find each sum or difference.5x2−2x−24+xx−6

Short Answer

Step by step solution

Step 1. Find LCD.

Step 2. Factor.

Step 3. Write using LCD.

Step 4. Simplify.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Logic and Functions

Geometry

Mechanics Maths

Statistics

Study anywhere. Anytime. Across all devices.

Find each sum or difference.
$\frac{5}{x^{2} - 2 x - 24} + \frac{x}{x - 6}$