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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. 45 (page 652)

In the following exercises, divide the rational expressions.
$\frac{3 s^{2}}{s^{2} - 16} 梅 \frac{s^{3} - 4 s^{2} + 16 s}{s^{3} - 64}$

Short Answer

Expert verified

The simplified expression is $\frac{3 s^{3}}{{(s - 4)}^{2} (s + 4)} .$

Step by step solution

01

Step 1. Given Information

$\frac{3 s^{2}}{s^{2} - 16} 梅 \frac{s^{3} - 4 s^{2} + 16 s}{s^{3} - 64}$

\frac{3 s^{2}}{s^{2} - 16} 脳 \frac{s^{3} - 4 s^{2} + 16 s}{s^{3} - 64}

02

Step 2. Factors the numerators and denominators

$\frac{3 s^{2}}{(s - 4) (s + 4)} 脳 \frac{s (s^{2} - 4 s + 16)}{s^{3} - 4^{3}} = \frac{3 s^{2}}{(s - 4) (s + 4)} 脳 \frac{s (s^{2} - 4 s + 16)}{(s - 4) (s^{2} - 4 s + 16)}$

03

Step 3. Multiply numerators and denominators and remove common factors

$= \frac{3 s 脳 s}{(s - 4) (s + 4)} 脳 \frac{s (s^{2} - 4 s + 16)}{(s - 4) (s^{2} - 4 s + 16)} = \frac{3 s^{3}}{{(s - 4)}^{2} (s + 4)}$

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Most popular questions from this chapter

The distance a moving body travels, $d$ , varies directly with the time, $t$ , it moves. The train travels 100 miles in 2 hours.

Write the equation that relates $d a n d t$ .
How many miles would it travel in 5 hours?

For the following exercises, perform the indicated operations.

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

Solve each rational function inequality and write the solution in interval notation. Given the function $R (x) = \frac{(x - 6)}{(x + 2)}$ , find the values of x that make the function less than or equal to 0.

Solve the rational equation $\frac{E}{c} = m^{2}$ for the variable c.

In the following exercise, perform the indicated operation:

$\frac{c}{c + 2} + \frac{5}{c - 2} - \frac{10 c}{c^{2} - 4}$

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