Chapter 8: Q. 8.113 (page 964)

Simplify: $\frac{\frac{3}{x^{2} + 7 x + 10}}{\frac{4}{x + 2} + \frac{1}{x + 5}}$

Short Answer

Expert verified

The simplified form of the given expression is $\frac{3}{5 x + 22}$ .

Step by step solution

Step 1. Given information.

The given expression is:

$\frac{\frac{3}{x^{2} + 7 x + 10}}{\frac{4}{x + 2} + \frac{1}{x + 5}}$

Step 2. Rewrite the expression and then simplify.

The LCD of all the fractions in the whole expression is $(x + 2) (x + 5)$ . Clear the fractions by multiplying the numerator and denominator by that LCD.

role="math" localid="1647924968789" $= \frac{(x + 2) (x + 5) \cdot (\frac{3}{x^{2} + 7 x + 10})}{(x + 2) (x + 5) \cdot (\frac{4}{x + 2} + \frac{1}{x + 5})} = \frac{(x + 2) (x + 5) \cdot \frac{3}{(x + 2) (x + 5)}}{(x + 2) (x + 5) \cdot \frac{4}{x + 2} + (x + 2) (x + 5) \cdot \frac{1}{x + 5}} = \frac{3}{4 (x + 5) + (x + 2)} = \frac{3}{4 x + 20 + x + 2} = \frac{3}{5 x + 22}$

Step 3. Conclusion.

The simplified form of the given expression is $\frac{3}{5 x + 22}$ .

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.

Simplify: $\frac{\frac{3}{x^{2} + 7 x + 10}}{\frac{4}{x + 2} + \frac{1}{x + 5}}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Rewrite the expression and then simplify.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Calculus

Statistics

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

Simplify:3x2+7x+104x+2+1x+5

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Rewrite the expression and then simplify.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Calculus

Statistics

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

Simplify: $\frac{\frac{3}{x^{2} + 7 x + 10}}{\frac{4}{x + 2} + \frac{1}{x + 5}}$