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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. 170 (page 680)

In the following exercises, simplify each complex rational expression by using the LCD.
$\frac{\frac{1}{6} + \frac{4}{15}}{\frac{3}{5} - \frac{1}{2}}$

Short Answer

Expert verified

The simplified expression is $\frac{13}{3}$ .

Step by step solution

01

Step 1. Given Information.

We have:

$\frac{\frac{1}{6} + \frac{4}{15}}{\frac{3}{5} - \frac{1}{2}}$

02

Step 2. Simplify the numerator.

The numerator is $\frac{1}{6} + \frac{4}{15}$ .

The least common divisor (LCD) of $6, 15$ is $30 .$

Adjust the fractions based on the LCD:

$= \frac{5}{30} + \frac{8}{30} = \frac{5 + 8}{30} = \frac{13}{30}$

03

Step 3. Simplify the denominator.

The denominator is $\frac{3}{5} - \frac{1}{2}$ .

The least common divisor (LCD) of $5, 2$ is $10 .$

Adjust the fractions based on the LCD:

$= \frac{6}{10} - \frac{5}{10} = \frac{6 - 5}{10} = \frac{1}{10}$

04

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

We have:

$\frac{\frac{1}{6} + \frac{4}{15}}{\frac{3}{5} - \frac{1}{2}} = \frac{\frac{13}{30}}{\frac{1}{10}}$

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

$= \frac{13 路鈥� 10}{30 路鈥� 1} = \frac{13}{3}$

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Most popular questions from this chapter

In the following exercises, divide the rational expressions.

$\frac{\frac{2 a^{2} - a - 21}{5 a + 20}}{\frac{a^{2} + 7 a + 12}{a^{2} + 8 a + 16}}$

Determine the values for which the rational expression is undefined.

$\frac{5 x^{2} y^{2}}{8 y}$

Simplify the complex rational expression by writing it as division:

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

For the following exercises, perform the indicated operations.
$\frac{12 p^{2} + 3 p}{p + 3} 梅 \frac{p^{2} + 2 p - 63}{p^{2} - p - 12} . \frac{p - 7}{9 p^{3} - 9 p^{2}}$

Simplify the complex rational expression by writing it as a division:

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

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