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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q7.49TI. (page 672)

Simplify the complex rational expression by writing it as a division:
$\frac{\frac{1}{2} + \frac{2}{3}}{\frac{5}{6} + \frac{1}{12}}$

Short Answer

Expert verified

$\frac{14}{11}$

Step by step solution

01

Step 1. Given information.

The following rational expression is given:

$\frac{\frac{1}{2} + \frac{2}{3}}{\frac{5}{6} + \frac{1}{12}}$

02

Step 2. Simplification of the rational expression.

Find the LCD and add the numerator and the denominator terms:

$\frac{\frac{1.3}{2.3} + \frac{2.2}{3.2}}{\frac{5.2}{6.2} + \frac{1}{12}}$

Simplify the numerator and the denominator:

$\frac{\frac{3}{6} + \frac{4}{6}}{\frac{10}{12} + \frac{1}{12}} \frac{\frac{7}{6}}{\frac{11}{12}}$

Rewrite as a division problem:

$\frac{7}{6} 梅 \frac{11}{12}$

Rewrite as the product of the first with the reciprocal of the second:

$\frac{7}{6} . \frac{12}{11}$

Factor, cancel out the common factors from the numerator and the denominator and then simplify:

$\frac{7}{6} . \frac{2.6}{11} \frac{14}{11}$

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