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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 8: Q. 534 (page 1025)

In the following exercises, divide.
$\frac{r^{2} - 16}{4} 梅 \frac{r^{3} - 64}{2 r^{2} + 8 r + 32}$

Short Answer

Expert verified

The answer is $\frac{r + 4}{2} .$

Step by step solution

01

Step 1. Given Information.

The given expression is $\frac{r^{2} - 16}{4} 梅 \frac{r^{3} - 64}{2 r^{2} + 8 r + 32} .$

02

Step 2. Divide.

To divide, rewrite the division as the product of the first rational expression and the reciprocal of the second.

$= \frac{r^{2} - 16}{4} 路 \frac{2 r^{2} + 8 r + 32}{r^{3} - 64}$

03

Step 3. Simplify.

Factor the numerators and denominators and then multiply.

$= \frac{(r - 4) (r + 4)}{2 路 2} 路 \frac{2 (r^{2} + 4 r + 16)}{(r - 4) (r^{2} + 4 r + 16)} = \frac{(r - 4) (r + 4) 路 2 (r^{2} + 4 r + 16)}{2 路 2 路 (r - 4) (r^{2} + 4 r + 16)}$

Now, simplify by dividing out common factors.

$= \frac{(r - 4) (r + 4) 路 2 (r^{2} + 4 r + 16)}{2 路 2 路 (r - 4) (r^{2} + 4 r + 16)} = \frac{r + 4}{2}$

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