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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. 171 (page 680)

In the following exercises, simplify each complex rational expression by using the LCD.
$\frac{\frac{c}{d} + \frac{1}{d}}{\frac{1}{d} - \frac{d}{c}}$

Short Answer

Expert verified

The simplified expression is $\frac{(c + 1) c}{c - d^{2}}$ .

Step by step solution

01

Step 1. Given Information.

We have:

$\frac{\frac{c}{d} + \frac{1}{d}}{\frac{1}{d} - \frac{d}{c}}$

02

Step 2. Simplify the numerator.

The numerator is $\frac{c}{d} + \frac{1}{d}$ .

The least common divisor (LCD) is $d .$

Apply fraction rule: $\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}$

$= \frac{c + 1}{d}$

03

Step 3. Simplify the denominator.

The denominator is $\frac{1}{d} - \frac{d}{c}$ .

The least common divisor (LCD) is $d c .$

$= \frac{c}{d c} - \frac{d^{2}}{d c} = \frac{c - d^{2}}{d c}$

04

Step 4. Substitute the simplified numerator and denominator into the original expression.

We have:

$\frac{\frac{c}{d} + \frac{1}{d}}{\frac{1}{d} - \frac{d}{c}} = \frac{\frac{c + 1}{d}}{\frac{c - d^{2}}{c d}}$

Apply fraction rule: $\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a 路鈥� d}{b 路鈥� c}$

$= \frac{(c + 1) c d}{d (c - d^{2})} = \frac{(c + 1) c}{c - d^{2}}$

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Most popular questions from this chapter

Simplify the complex rational expression by using the LCD:

$\frac{\frac{3}{x + 2}}{\frac{5}{x - 2} - \frac{3}{x^{2} - 4}}$

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