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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. 187 (page 681)

In the following exercises, simplify each complex rational expression using either method.
$\frac{\frac{3}{4} - \frac{2}{7}}{\frac{1}{2} + \frac{5}{14}}$

Short Answer

Expert verified

The simplified form is $\frac{13}{64}$ .

Step by step solution

01

Step 1. Given.

The given complex rational expression is: $\frac{\frac{3}{4} - \frac{2}{7}}{\frac{1}{2} + \frac{5}{14}}$ .

02

Step 2. To find

We have to simplify each complex rational expression by using either method.

03

Step 3. Calculation

LCM of the denominators is = 28. Multiply numerator and denominator by it to simplify.

$\frac{\frac{3}{4} - \frac{2}{7}}{\frac{1}{2} + \frac{5}{14}} = \frac{\frac{3}{4} (28) - \frac{2}{7} (28)}{\frac{1}{2} (28) + \frac{5}{14} (28)} = \frac{3 (7) - 2 (4)}{1 (14) + 5 (10)} = \frac{21 - 8}{14 + 50} = \frac{13}{64}$

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