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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. 66 (page 653)

For the following exercises, find $R (x) = f (x) g (x)$ where $f (x) a n d g (x)$ are given.
$f (x) = \frac{2 x^{2} + 8 x}{x^{2} - 9 x + 20} a n d g (x) = \frac{x - 5}{x^{2}}$

Short Answer

Expert verified

The value of $R (x) = \frac{2 (x + 4)}{x (x - 4)} .$

Step by step solution

01

Step 1. Given Information

$f (x) = \frac{2 x^{2} + 8 x}{x^{2} - 9 x + 20} a n d g (x) = \frac{x - 5}{x^{2}}$

02

Step 2. Factor each numerator and denominator

$R (x) = \frac{2 x^{2} + 8 x}{x^{2} - 9 x + 20} . \frac{x - 5}{x^{2}} R (x) = \frac{2 x (x + 4)}{(x - 4) (x - 5)} . \frac{x - 5}{x . x}$

03

Step 3. Multiply numerators and denominators

$R (x) = \frac{2 x (x + 4) (x - 5)}{x . x (x - 4) (x - 5)}$

04

Step 4. Remove common factors and simplify

$R (x) = \frac{2 (x + 4)}{x (x - 4)}$

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Most popular questions from this chapter

For the following exercises, find $R (x) = f (x) . g (x)$ where $f (x) a n d g (x)$ are given.

$f (x) = \frac{4 x}{x^{2} - 3 x - 10} a n d g (x) = \frac{x^{2} - 25}{8 x^{2}}$

In the following exercises, find the domain of each function.

$R (x) = \frac{8 x^{2} - 32 x}{2 x^{2} - 6 x - 80}$

In the following exercises, solve each rational inequality and write the solution in interval notation.

$\frac{5}{(x - 1)} 鈮� \frac{4}{(x + 2)}$

Simplify the complex rational expression by LCD:

$\frac{\frac{1}{2} + \frac{1}{5}}{\frac{1}{10} + \frac{1}{5}}$

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?

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