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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. 46 (page 652)

In the following exercises, divide the rational expressions.
$\frac{r^{2} - 9}{15} 梅 \frac{r^{3} - 27}{5 r^{2} + 15 r + 45}$

Short Answer

Expert verified

The simplified expression is $\frac{r + 3}{3} .$

Step by step solution

01

Step 1. Given Information

$\frac{r^{2} - 9}{15} 梅 \frac{r^{3} - 27}{5 r^{2} + 15 r + 45} = \frac{r^{2} - 9}{15} 脳 \frac{5 r^{2} + 15 r + 45}{r^{3} - 27}$

02

Step 2. Factor the numerators and denominators

$= \frac{(r - 3) (r + 3)}{15} 脳 \frac{5 (r^{2} + 3 r + 9)}{(r - 3) (r^{2} + 3 r + 9)} = \frac{5 (r - 3) (r + 3) (r^{2} + 3 r + 9)}{15 (r - 3) (r^{2} + 3 r + 9)}$

03

Step 3. Remove the common factor and simplify

$= \frac{r + 3}{3}$

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Most popular questions from this chapter

For the following exercises, perform the indicated operations. $\frac{10 m^{2} + 80 m}{3 m - 9} . \frac{m^{2} + 4 m - 21}{m^{2} - 9 m + 20} 梅 \frac{5 m^{2} + 10 m}{2 m - 10}$

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