Chapter 8: Q. 8.126 (page 975)

Solve :
$\frac{3}{x + 8} - \frac{2}{x - 2} = 1$

Short Answer

Expert verified

$x = - 2, - 3$ .

Step by step solution

Step 1. Given information.

To solve $\frac{3}{x + 8} - \frac{2}{x - 2} = 1$ .

Step 2. Solve by taking LCD.

We get

$\frac{3}{x + 8} - \frac{2}{x - 2} = 1; x \neq - 8, x \neq 2$

Take LCD and multiply it to both sides.

$(x - 2) (x + 8) [\frac{3}{x + 8} - \frac{2}{x - 2}] = 1 [(x + 8) (x - 2)] 3 (x - 2) - 2 (x + 8) = (x - 2) (x + 8) 3 x - 6 - 2 x - 16 = x^{2} - 2 x + 8 x - 16 x - 22 = x^{2} + 6 x - 16 0 = x^{2} + 5 x + 6$

Step 3. Factorize and use zero product property.

On simplifying,

$x^{2} + 5 x + 6 = 0 x^{2} + 2 x + 3 x + 6 = 0 x (x + 2) + 3 (x + 2) = 0 (x + 2) (x + 3) = 0 x = - 2 o r x = - 3$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Solve :
$\frac{3}{x + 8} - \frac{2}{x - 2} = 1$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve by taking LCD.

Step 3. Factorize and use zero product property.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Geometry

Mechanics Maths

Decision Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve :3x+8-2x-2=1

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve by taking LCD.

Step 3. Factorize and use zero product property.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Geometry

Mechanics Maths

Decision Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve :
$\frac{3}{x + 8} - \frac{2}{x - 2} = 1$