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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. 431 (page 737)

In the following exercise, simplify.
$\frac{\frac{1}{3} + \frac{1}{8}}{\frac{1}{4} + \frac{1}{12}}$

Short Answer

Expert verified

The solution is $\frac{11}{8}$

Step by step solution

01

Step 1. Given information

$\frac{\frac{1}{3} + \frac{1}{8}}{\frac{1}{4} + \frac{1}{12}}$

02

Step2. Simplify

The LCD of all fractions in the complex rational expression is $24 脳 3$ .

Multiply the numerator and denominator by the LCD.

role="math" localid="1646724877348" $\frac{(24 脳 3) (\frac{1}{3} + \frac{1}{8})}{(24 脳 3) (\frac{1}{4} + \frac{1}{12})}$

Distribute in the numerator and denominator and simplify

$= \frac{((24 脳 3) \frac{1}{3} + (24 脳 3) \frac{1}{8})}{((24 脳 3) \frac{1}{4} + (24 脳 3) \frac{1}{12})} = \frac{24 + 9}{18 + 6} = \frac{11}{8}$

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