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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. 169 (page 680)

In the following exercises, simplify each complex rational expression by using the LCD.
$\frac{\frac{5}{6} + \frac{2}{9}}{\frac{7}{18} - \frac{1}{3}}$

Short Answer

Expert verified

The simplified expression is $19$ .

Step by step solution

01

Step 1. Given Information.

We have:

$\frac{\frac{5}{6} + \frac{2}{9}}{\frac{7}{18} - \frac{1}{3}}$

02

Step 2. Simplify the numerator.

The numerator is $\frac{5}{6} + \frac{2}{9}$ .

The least common divisor (LCD) of $6, 9$ is $18 .$

Adjust the fractions based on the LCD:

$= \frac{15}{18} + \frac{4}{18} = \frac{15 + 4}{18} = \frac{19}{18}$

03

Step 3. Simplify the denominator.

The denominator is $\frac{7}{18} - \frac{1}{3}$ .

The least common divisor (LCD) of $18, 3$ is $18 .$

Adjust the fractions based on the LCD:

$= \frac{7}{18} - \frac{6}{18} = \frac{7 - 6}{18} = \frac{1}{18}$

04

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

We have:

$\frac{\frac{5}{6} + \frac{2}{9}}{\frac{7}{18} - \frac{1}{3}} = \frac{\frac{19}{18}}{\frac{1}{18}}$

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

$= \frac{19 路鈥� 18}{18 路鈥� 1} = 19$

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Most popular questions from this chapter

In the following exercises, multiply the rational expressions.

$\frac{28 - 4 b}{3 b - 3} . \frac{b^{2} + 8 b - 9}{b^{2} - 49}$

In the following exercise, find

(a) $R (x) = f (x) + g (x)$

(b) $R (x) = f (x) - g (x)$ :

$f (x) = \frac{6 x}{x^{2} - 64} g (x) = \frac{3}{x - 8}$

In the following exercise, find

(a) $R (x) = f (x) + g (x)$

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$f (x) = \frac{- 5 x - 5}{x^{2} + x - 6} g (x) = \frac{x + 1}{2 - x}$

Multiply $\frac{5}{8} . \frac{4}{15}$

For the following exercises, find $R (x) = f (x) g (x)$ where $f (x) a n d g (x)$ are given.

$f (x) = \frac{2 x^{2} + 8 x}{x^{2} - 9 x + 20} a n d g (x) = \frac{x - 5}{x^{2}}$

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