Chapter 8: Q 8.97 (page 952)

Simplify: $\frac{v}{v + 1} + \frac{3}{v - 1} - \frac{6}{v^{2} - 1}$

Short Answer

Expert verified

The simplification of the rational expression is $\frac{v^{2} + 2 v - 3}{(v + 1) (v - 1)}$ .

Step by step solution

Given information

The given rational expression is $\frac{v}{v + 1} + \frac{3}{v - 1} - \frac{6}{v^{2} - 1}$ .

The simplification of the rational expression

$\frac{v}{v + 1} + \frac{3}{v - 1} - \frac{6}{(v - 1) (v + 1)}$

The LCD of the expression is $(v + 1) (v - 1)$ .

Rewrite each rational expression as an equivalent rational expression with the LCD.

$= \frac{v (v - 1)}{(v + 1) (v - 1)} + \frac{3 (v + 1)}{(v - 1) (v + 1)} - \frac{6}{(v + 1) (v - 1)} = \frac{v^{2} - v}{(v + 1) (v - 1)} + \frac{3 v + 3}{(v + 1) (v - 1)} - \frac{6}{(v + 1) (v - 1)} S i m p l i f y = \frac{v^{2} - v + 3 v + 3 - 6}{(v + 1) (v - 1)} = \frac{v^{2} + 2 v - 3}{(v + 1) (v - 1)} (v^{2} + 2 v - 3) cannot factorized further . \frac{v^{2} + 2 v - 3}{(v + 1) (v - 1)}$

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: $\frac{v}{v + 1} + \frac{3}{v - 1} - \frac{6}{v^{2} - 1}$

Short Answer

Step by step solution

Given information

The simplification of the rational expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Logic and Functions

Pure Maths

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Simplify:vv+1+3v-1-6v2-1

Short Answer

Step by step solution

Given information

The simplification of the rational expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Logic and Functions

Pure Maths

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Simplify: $\frac{v}{v + 1} + \frac{3}{v - 1} - \frac{6}{v^{2} - 1}$