Q. 7.43 Simplify:聽vv+1+3v-1-6v2-1.... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 7.43 (page 665)

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

Short Answer

Expert verified

The simplified expression is $\frac{v + 3}{v + 1}$ .

Step by step solution

Step 1. Given Information

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

Step 2. Express with common denominator

Factor the denominators of the given expression.

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

The LCD of the terms of obtained expression is $(v + 1) (v - 1)$ .
Multiply the numerator and denominator of first term by $(v - 1)$ and second term by $(v + 1)$ .

role="math" localid="1645094797074" $\frac{v (v - 1)}{(v + 1) (v - 1)} + \frac{3 (v + 1)}{(v - 1) (v + 1)} - \frac{6}{(v + 1) (v - 1)} = \frac{v^{2} - v}{(v + 1) (v - 1)} + \frac{3 v + 3}{(v - 1) (v + 1)} - \frac{6}{(v + 1) (v - 1)}$

Step 3. Simplify

As the denominator is the same for both the terms, perform desired operations in the numerator and place it over the common denominator.

$\frac{v^{2} - v + 3 v + 3 - 6}{(v + 1) (v - 1)} = \frac{v^{2} + 2 v - 3}{(v + 1) (v - 1)}$

Factor the numerator and cancel the common factors from numerator and denominator.

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

So, the resultant expression is $\frac{v + 3}{v + 1}$ .

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91影视

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Express with common denominator

Step 3. Simplify

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91影视

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Express with common denominator

Step 3. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Geometry

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

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