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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q7.53TI. (page 674)

Simplify the complex rational expression by writing it as division:
$\frac{b - \frac{3 b}{b + 5}}{\frac{2}{b + 5} + \frac{1}{b - 5}}$

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given information.

The following complex rational expression is given:

$\frac{b - \frac{3 b}{b + 5}}{\frac{2}{b + 5} + \frac{1}{b - 5}}$

02

Step 2. Simplification of the complex rational expression.

Simplify the numerator and the denominator by finding the common denominators:

$\frac{\frac{b (b + 5)}{(b + 5)} - \frac{3 b}{b + 5}}{\frac{2 (b - 5)}{(b + 5) (b - 5)} + \frac{1 (b + 5)}{(b - 5) (b + 5)}}$

Simplify the numerator and the denominator:

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

Write as a division problem:

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

Write as the product of the numerator and the reciprocal of the denominator:

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

Cancel the common factors from the numerator and the denominator and simplify:

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

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Most popular questions from this chapter

In the following exercises, divide the rational expressions.

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