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

Step 1. Given information.

The following expression is given:

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

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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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

Step by step solution

Step 1. Given information.

Step 2. Performing the subtraction operation.

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In the following exercise, perform the indicated operation:32x2+5x+2-12x2+3x+1

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Performing the subtraction operation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Decision Maths

Probability and Statistics

Calculus

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

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