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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. 156 (page 680)

In the following exercises, simplify each complex rational expression by writing it as division.
$\frac{\frac{1}{2} + \frac{3}{4}}{\frac{3}{5} + \frac{7}{10}}$

Short Answer

Expert verified

The required solution is $\frac{25}{26}$ .

Step by step solution

01

Step 1. Given Information.

We have:

$\frac{\frac{1}{2} + \frac{3}{4}}{\frac{3}{5} + \frac{7}{10}}$

02

Step 2. Simplify the numerator:

The numerator is $\frac{1}{2} + \frac{3}{4}$ .

The least common multiplier of $2, 4$ is $4 .$

$= \frac{2}{4} + \frac{3}{4} = \frac{2 + 3}{4} = \frac{5}{4}$

03

Step 3. Simplify the denominator.

Here, the denominator is $\frac{3}{5} + \frac{7}{10}$ .

The least common multiplier of $5, 10$ is $50 .$

$= \frac{6}{10} + \frac{7}{10} = \frac{6 + 7}{10} = \frac{13}{10}$

04

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

We have:

$\frac{\frac{1}{2} + \frac{3}{4}}{\frac{3}{5} + \frac{7}{10}} = \frac{\frac{5}{4}}{\frac{13}{10}}$

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

$= \frac{5 路鈥� 10}{4 路鈥� 13} = \frac{25}{26}$

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Most popular questions from this chapter

Simplify the complex rational expression by writing it as division:

$\frac{\frac{1}{x^{2} - 7 x + 12}}{\frac{2}{x - 4}}$

In the following exercises, solve each rational inequality and write the solution in interval notation.

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