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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. 37 (page 652)

In the following exercises, multiply the rational expressions.
$\frac{28 - 4 b}{3 b - 3} . \frac{b^{2} + 8 b - 9}{b^{2} - 49}$

Short Answer

Expert verified

The multiplication of the expressions is $\frac{- 4 (b + 9)}{(b + 7)} .$

Step by step solution

01

Step 1. Given information

The rational expression is $\frac{28 - 4 b}{3 b - 3} . \frac{b^{2} + 8 b - 9}{b^{2} - 49}$

02

Step 2. Factor each numerator and denominator completely.

Factor $28 - 4 b$ and $b^{2} - 49 .$

$28 - 4 b = 4 (7 - b)$ and

$b^{2} - 49 = (b - 7) (b + 7)$ and

$b^{2} + 8 b - 9 = b^{2} + 9 b - b - 9 = b (b + 9) - 1 (b + 9) = (b + 9) (b - 1)$

03

Step 3. Multiply the numerators and denominators.

$\frac{28 - 4 b}{3 b - 3} . \frac{b^{2} + 8 b - 9}{b^{2} - 49} = \frac{4 (7 - b)}{3 (b - 1)} . \frac{(b + 9) (b - 1)}{(b - 7) (b + 7)} = \frac{- 4 (b - 7) (b + 9)}{(b - 7) (b + 7)} = \frac{- 4 (b + 9)}{(b + 7)} .$

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Most popular questions from this chapter

For the following exercises, perform the indicated operations.

$\frac{6 q + 3}{9 q^{2} - 9 q} 梅 \frac{q^{2} + 14 q + 33}{q^{2} + 4 q - 5} . \frac{4 q^{2} + 12 q}{12 q + 6}$

For the following exercises, perform the indicated operations.

$\frac{4 n^{2} + 32 n}{3 n + 2} . \frac{3 n^{2} - n - 2}{n^{2} + n - 30} 梅 \frac{108 n^{2} - 24 n}{n + 6}$

Divide $\frac{y^{2} - 16}{4} 梅 \frac{y^{3} - 64}{2 y^{2} + 8 y + 32}$

Simplify the complex rational expression by writing it as division:

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

A telephone pole casts a shadow that is 50 feet long. Nearby, an 8-foot tall traffic sign casts a shadow that is 10 feet long. How tall is the telephone pole?

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