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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q136E. (page 668)

In the following exercise, perform the indicated operation:
$\frac{3}{2 x^{2} + 5 x + 2} - \frac{1}{2 x^{2} + 3 x + 1}$

Short Answer

Expert verified

$\frac{1}{(x + 2) (x + 1)}$

Step by step solution

01

Step 1. Given information.

The following expression is given:

$\frac{3}{2 x^{2} + 5 x + 2} - \frac{1}{2 x^{2} + 3 x + 1}$

02

Step 2. Performing the subtraction operation.

Factor the denominator:

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

Find out the LCD:

$(2 x + 1) (x + 2) (x + 1)$

Rewrite the expression with LCD at the denominator:

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

Simplify:

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

Cancel the common factors from the numerator and the denominator:

$\frac{1}{(x + 2) (x + 1)}$

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Most popular questions from this chapter

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