Chapter 11: Q. 7.12 (page 1069)

Simplify $\frac{4 b^{2} + 7 b - 2}{1 - b^{2}} \cdot \frac{b^{2} - 2 b + 1}{4 b^{2} + 15 b - 4}$ .

Short Answer

Expert verified

The simplest form of the given expression is

$- \frac{(b - 1) (b + 2)}{(b + 1) (b + 4)} .$

Step by step solution

Step 1. Given information

The given expression is $\frac{4 b^{2} + 7 b - 2}{1 - b^{2}} \cdot \frac{b^{2} - 2 b + 1}{4 b^{2} + 15 b - 4}$

Step 2. Simplify

$\frac{4 b^{2} + 7 b - 2}{1 - b^{2}} \cdot \frac{b^{2} - 2 b + 1}{4 b^{2} + 15 b - 4} = \frac{(4 b - 1) (b + 2)}{- (b - 1) (b + 1)} \cdot \frac{(b - 1) (b - 1)}{(4 b - 1) (b + 4)} = - \frac{(b + 2)}{(b + 1)} \cdot \frac{(b - 1)}{(b + 4)} = - \frac{(b - 1) (b + 2)}{(b + 1) (b + 4)}$

Hence, the simplified expression is $- \frac{(b - 1) (b + 2)}{(b + 1) (b + 4)} .$

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 $\frac{4 b^{2} + 7 b - 2}{1 - b^{2}} \cdot \frac{b^{2} - 2 b + 1}{4 b^{2} + 15 b - 4}$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Geometry

Applied Mathematics

Decision Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Simplify4b2+7b-21-b2·b2-2b+14b2+15b-4.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Geometry

Applied Mathematics

Decision Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Simplify $\frac{4 b^{2} + 7 b - 2}{1 - b^{2}} \cdot \frac{b^{2} - 2 b + 1}{4 b^{2} + 15 b - 4}$ .