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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. 155 (page 680)

In the following exercises, simplify each complex rational expression by writing it as division.
$\frac{\frac{1}{2} + \frac{5}{6}}{\frac{2}{3} + \frac{7}{9}}$

Short Answer

Expert verified

The required solution is $\frac{12}{13}$ .

Step by step solution

01

Step 1. Given Information.

We have:

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

02

Step 2. Simplify the numerator:

The numerator is $\frac{1}{2} + \frac{5}{6}$ :

The least common multiplier of $2, 6$ is $6 .$

Adjust the fractions based on the LCM:

$= \frac{3}{6} - \frac{5}{6}$

role="math" localid="1644998162915" $= \frac{3 + 5}{6} = \frac{8}{6} = \frac{4}{3}$

03

Step 3. Simplify the denominator.

Here, the denominator is $\frac{2}{3} + \frac{7}{9}$ .

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

Adjust the fractions based on the LCM:

$= \frac{6}{9} + \frac{7}{9} = \frac{6 + 7}{9} = \frac{13}{9}$

04

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

We have:

$\frac{\frac{1}{2} + \frac{5}{6}}{\frac{2}{3} + \frac{7}{9}} = \frac{\frac{4}{3}}{\frac{13}{9}}$

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

$= \frac{4 路鈥� 9}{3 路鈥� 13} = \frac{12}{13}$

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Most popular questions from this chapter

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

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