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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q7.56TI. (page 1069)

Simplify the complex rational expression by LCD:
$\frac{\frac{1}{4} + \frac{3}{8}}{\frac{1}{2} - \frac{5}{16}}$

Short Answer

Expert verified

$\frac{10}{3}$

Step by step solution

01

Step 1. Given information.

The following complex rational expression is given:

$\frac{\frac{1}{4} + \frac{3}{8}}{\frac{1}{2} - \frac{5}{16}}$

02

Step 2. Simplification of the rational expression.

The LCD of all the fractions in the whole expression is 16.

Multiply both the numerator and the denominator by 16:

$\frac{16 (\frac{1}{4} + \frac{3}{8})}{16 (\frac{1}{2} - \frac{5}{16})}$

Distribute:

$\frac{16 路 \frac{1}{4} + 16 路 \frac{3}{8}}{16 路 \frac{1}{2} - 16 路 \frac{5}{16}}$

Simplify:

$\frac{4 + 6}{8 - 5} \frac{10}{3}$

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