Q. 7.41 Subtract:聽3b2-4b-5-2b2-6b+5.... [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. 7.41 (page 664)

Subtract: $\frac{3}{b^{2} - 4 b - 5} - \frac{2}{b^{2} - 6 b + 5}$ .

Short Answer

Expert verified

The resultant expression is $\frac{1}{(b + 1) (b - 1)}$ .

Step by step solution

Step 1. Given Information

The given expression is $\frac{3}{b^{2} - 4 b - 5} - \frac{2}{b^{2} - 6 b + 5}$ .

Step 2. Express with common denominator

Factor the denominators of the given expression.

$\frac{3}{(b - 5) (b + 1)} - \frac{2}{(b - 5) (b - 1)}$

The LCD of the terms of obtained expression is $(b - 5) (b + 1) (b - 1)$ .
Multiply the numerator and denominator of first term by $(b - 1)$ and second term by $(b + 1)$ .

role="math" localid="1645088626910" $\frac{3 (b - 1)}{(b - 5) (b + 1) (b - 1)} - \frac{2 (b + 1)}{(b - 5) (b - 1) (b + 1)} = \frac{3 b - 3}{(b - 5) (b + 1) (b - 1)} - \frac{2 b + 2}{(b - 5) (b - 1) (b + 1)}$

Step 3. Simplify

As the denominator is the same for both the terms, subtract the numerator and place it over the common denominator.

$\frac{3 b - 3 - 2 b - 2}{(b - 5) (b + 1) (b - 1)} = \frac{b - 5}{(b - 5) (b + 1) (b - 1)}$

Cancel the common factors from numerator and denominator.

$\frac{b - 5}{(b - 5) (b + 1) (b - 1)} = \frac{1}{(b + 1) (b - 1)}$

So, the resultant expression is $\frac{1}{(b + 1) (b - 1)}$ .

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91影视

Subtract: $\frac{3}{b^{2} - 4 b - 5} - \frac{2}{b^{2} - 6 b + 5}$ .

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

Subtract:3b2-4b-5-2b2-6b+5.

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

Probability and Statistics

Calculus

Mechanics Maths

Geometry

Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Subtract: $\frac{3}{b^{2} - 4 b - 5} - \frac{2}{b^{2} - 6 b + 5}$ .