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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. 63 (page 653)

For the following exercises, find $R (x) = f (x) . g (x)$ where $f (x) a n d g (x)$ are given.
localid="1644679377284" $f (x) = \frac{6 x^{2} - 12 x}{x^{2} + 7 x - 18} a n d g (x) = \frac{x^{2} - 81}{3 x^{2} - 27 x}$

Short Answer

Expert verified

The value of $R (x) = 2$

Step by step solution

01

Step 1. Given Information

$f (x) = \frac{6 x^{2} - 12 x}{x^{2} + 7 x - 18} a n d g (x) = \frac{x^{2} - 81}{3 x^{2} - 27 x}$

02

Step 2. Factor each numerator and denominator

$R (x) = \frac{6 x (x - 2)}{(x + 9) (x - 2)} . \frac{(x - 9) (x + 9)}{3 x (x - 9)}$

$R (x) = \frac{6 x (x - 2) (x - 9) (x + 9)}{3 x (x + 9) (x - 2) (x - 9)}$

03

Step 3. Remove common factors and simplify

$R (x) = \frac{6}{3} = 2$

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