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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. 151 (page 680)

In the following exercises, simplify each complex rational expression by writing it as division.
$\frac{\frac{2 a}{a + 4}}{\frac{4 a^{2}}{a^{2} - 16}}$

Short Answer

Expert verified

The simplified expression is $\frac{a - 4}{2 a}$ .

Step by step solution

01

Step 1. Given Information.

We have:

$\frac{\frac{2 a}{a + 4}}{\frac{4 a^{2}}{a^{2} - 16}}$

02

Step 2. Find the LCD of all fractions in complex rational expression.

The least common divisor (LCD) is $(a - 4) (a + 4) .$

Multiply the numerator and denominator by the LCD:

$= \frac{(a - 4) (a + 4) (\frac{2 a}{a + 4})}{(a - 4) (a + 4) (\frac{4 a^{2}}{a^{2} - 16})}$

03

Step 3. Simplify the expression.

Further, calculate:

$= \frac{(a - 4) (a + 4) (\frac{2 a}{(a + 4)})}{(a - 4) (a + 4) (\frac{4 a^{2}}{(a - 4) (a + 4)})} = \frac{(a - 4) 2 a}{4 a^{2}} = \frac{a - 4}{2 a}$

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