Chapter 11: Q. 39 (page 1069)

In the following exercises, multiply the rational expressions. $\frac{5 c^{2} + 9 c + 2}{c^{2} - 25} . \frac{c^{2} + 10 c + 25}{3 c^{2} - 14 c - 5}$

Short Answer

Expert verified

The simplified expression is $\frac{(5 c^{2} + 9 c + 2) (c + 5)}{(3 c + 1) {(c - 5)}^{2}} .$

Step by step solution

Step 1. Given Information.

$\frac{5 c^{2} + 9 c + 2}{c^{2} - 25} . \frac{c^{2} + 10 c + 25}{3 c^{2} - 14 c - 5}$

Step 2. Factor each numerator and denominator completely

$c^{2} + 10 c + 25 = (c + 5) (c + 5) c^{2} - 25 = (c - 5) (c + 5) 3 c^{2} - 14 c - 5 = (3 c + 1) (c - 5)$

Then, multiply the numerators and denominators.

$\frac{5 c^{2} + 9 c + 2}{c^{2} - 25} . \frac{c^{2} + 10 c + 25}{3 c^{2} - 14 c - 5} = \frac{5 c^{2} + 9 c + 2}{(c - 5) (c + 5)} . \frac{(c + 5) (c + 5)}{(3 c + 1) (c - 5)}$

Step 3. Simplify by dividing out common factors

$\frac{(5 c^{2} + 9 c + 2) (c + 5)}{(3 c + 1) {(c - 5)}^{2}} .$

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.

In the following exercises, multiply the rational expressions. $\frac{5 c^{2} + 9 c + 2}{c^{2} - 25} . \frac{c^{2} + 10 c + 25}{3 c^{2} - 14 c - 5}$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Factor each numerator and denominator completely

Step 3. Simplify by dividing out common factors

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Logic and Functions

Geometry

Mechanics Maths

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, multiply the rational expressions.5c2+9c+2c2-25.c2+10c+253c2-14c-5

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Factor each numerator and denominator completely

Step 3. Simplify by dividing out common factors

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Logic and Functions

Geometry

Mechanics Maths

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, multiply the rational expressions. $\frac{5 c^{2} + 9 c + 2}{c^{2} - 25} . \frac{c^{2} + 10 c + 25}{3 c^{2} - 14 c - 5}$