Q. 7.39 Subtract:聽3x-1x2-5x-6-26-x.... [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. 7.39 (page 663)

Subtract: $\frac{3 x - 1}{x^{2} - 5 x - 6} - \frac{2}{6 - x}$ .

Short Answer

Expert verified

The resultant expression is $\frac{5 x + 1}{(x - 6) (x + 1)}$ .

Step by step solution

Step 1. Given Information

The given expression is $\frac{3 x - 1}{x^{2} - 5 x - 6} - \frac{2}{6 - x}$ .

Step 2. Rewrite the given expression

Factor the denominator of first term in the given expression.

$\frac{3 x - 1}{(x - 6) (x + 1)} - \frac{2}{6 - x}$

Since $(x - 6), (6 - x)$ are opposite in signs, multiply the numerator and denominator of the second term of the obtained expression by $- 1$ .

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

Step 3. Express with common denominator

The LCD of the terms of obtained expression is $(x - 6) (x + 1)$ .
Multiply the numerator and denominator of second term by $x + 1$ .

role="math" localid="1645085950232" $\frac{3 x - 1}{(x - 6) (x + 1)} + \frac{2 (x + 1)}{(x - 6) (x + 1)} = \frac{3 x - 1}{(x - 6) (x + 1)} + \frac{2 x + 2}{(x - 6) (x + 1)}$

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

$\frac{3 x - 1 + 2 x + 2}{(x - 6) (x + 1)} = \frac{5 x + 1}{(x - 6) (x + 1)}$

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91影视

Subtract: $\frac{3 x - 1}{x^{2} - 5 x - 6} - \frac{2}{6 - x}$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Rewrite the given expression

Step 3. Express with common denominator

One App. One Place for Learning.

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91影视

Subtract:3x-1x2-5x-6-26-x.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Rewrite the given expression

Step 3. Express with common denominator

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Logic and Functions

Probability and Statistics

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

Subtract: $\frac{3 x - 1}{x^{2} - 5 x - 6} - \frac{2}{6 - x}$ .