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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. 152 (page 680)

In the following exercises, simplify each complex rational expression by writing it as division.
$\frac{\frac{3 b}{b - 5}}{\frac{b^{2}}{b^{2} - 25}}$

Short Answer

Expert verified

The simplified expression is $\frac{3 (b + 5)}{b}$ .

Step by step solution

01

Step 1. Given Information.

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

The least common divisor is $(b - 5) (b + 5)$ .

Multiply the numerator and denominator by the LCD:

$= \frac{(b - 5) (b + 5) \frac{3 b}{b - 5}}{(b - 5) (b + 5) \frac{b^{2}}{b^{2} - 25}}$

02

Step 3. Simplify the expression

Further, calculate:

$= \frac{(b - 5) (b + 5) \frac{3 b}{(b - 5)}}{(b - 5) (b + 5) \frac{b^{2}}{(b - 5) (b + 5)}} = \frac{(b - 5) (b + 5) \frac{3 b}{(b - 5)}}{(b - 5) (b + 5) \frac{b^{2}}{(b - 5) (b + 5)}} = \frac{3 b (b + 5)}{b^{2}} = \frac{3 (b + 5)}{b}$

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