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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. 176 (page 680)

In the following exercises, simplify each complex rational expression by using the LCD.
$\frac{\frac{5}{y - 4}}{\frac{3}{y + 4} + \frac{2}{y^{2} - 16}}$

Short Answer

Expert verified

The simplified expression is $\frac{5 (y + 4)}{3 y - 10}$ .

Step by step solution

01

Step 1. Given Information.

We have:

$\frac{\frac{5}{y - 4}}{\frac{3}{y + 4} + \frac{2}{y^{2} - 16}}$

02

Step 2. Multiply the numerator and denominator by the LCD.

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

Multiply the numerator and denominator by $(y + 4) (y - 4)$ :

$= \frac{(y - 4) (y + 4) (\frac{5}{y - 4})}{(y - 4) (y + 4) (\frac{3}{y + 4} + \frac{2}{y^{2} - 16})}$

03

Step 3. Simplify the expression.

We have:

$= \frac{(y - 4) (y + 4) (\frac{5}{(y - 4)})}{(y - 4) (y + 4) (\frac{3}{y + 4} + \frac{2}{y^{2} - 4^{2}})} = \frac{(y - 4) (y + 4) (\frac{5}{(y - 4)})}{(y - 4) (y + 4) (\frac{3}{(y + 4)} + \frac{2}{(y - 4) (y + 4)})} = \frac{(y - 4) (y + 4) (\frac{5}{(y - 4)})}{(y - 4) (y + 4) \frac{3}{(y + 4)} + (y - 4) (y + 4) \frac{2}{(y - 4) (y + 4)}} = \frac{5 (y + 4)}{3 (y - 4) + 2} = \frac{5 y + 20}{3 y - 12 + 2} = \frac{5 y + 20}{3 y - 10} = \frac{5 (y + 4)}{3 y - 10}$

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Most popular questions from this chapter

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