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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. 157 (page 680)

In the following exercises, simplify each complex rational expression by writing it as division.
$\frac{\frac{2}{3} - \frac{1}{9}}{\frac{3}{4} + \frac{5}{6}}$

Short Answer

Expert verified

The required solutions is $\frac{20}{57}$ .

Step by step solution

01

Step 1. Given Information.

We have:

$\frac{\frac{2}{3} - \frac{1}{9}}{\frac{3}{4} + \frac{5}{6}}$

02

Step 2. Simplify the numerator:

The numerator is $\frac{2}{3} - \frac{1}{9}$ .

The least common multiplier of $3, 9$ is $9 .$

Adjust the fractions based on the LCM:

$= \frac{6}{9} - \frac{1}{9} = \frac{6 - 1}{9} = \frac{5}{9}$

03

Step 3. Simplify the denominator.

The denominator is $\frac{3}{4} + \frac{5}{6}$ .

The least common multiplier of $4, 6$ is $12 .$

Adjust the fractions based on the LCM:

$= \frac{9}{12} + \frac{10}{12} = \frac{9 + 10}{12} = \frac{19}{12}$

04

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

We have:

$\frac{\frac{2}{3} - \frac{1}{9}}{\frac{3}{4} + \frac{5}{6}} = \frac{\frac{5}{9}}{\frac{19}{12}}$

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

$= \frac{5 路鈥� 12}{9 路鈥� 19} = \frac{20}{57}$

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Simplify the complex rational expression by writing it as division:

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