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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. 7.21 (page 649)

Find $R (x) = f (x) 路 g (x)$ where $f (x) = \frac{3 x - 21}{x^{2} - 9 x + 14}$ and $g (x) = \frac{2 x^{2} - 8}{3 x + 6}$ .

Short Answer

Expert verified

The value of $R (x) = 2 .$

Step by step solution

01

Step 1. Given information

$f (x) = \frac{3 x - 21}{x^{2} - 9 x + 14}, g (x) = \frac{2 x^{2} - 8}{3 x + 6}$ and

$R (x) = f (x) 路 g (x)$

02

Step 2. Find R(x)

$R (x) = f (x) 路 g (x) R (x) = \frac{3 x - 21}{x^{2} - 9 x + 14} 路 \frac{2 x^{2} - 8}{3 x + 6} Usegivendata = \frac{3 (x - 7)}{(x - 7) (x - 2)} 路 \frac{2 (x - 2) (x + 2)}{3 (x + 2)} Factorizenumeratoranddenominator = \frac{3 路 2 (x - 7) (x - 2) (x + 2)}{3 (x - 7) (x - 2) (x + 2)} Multiplythenumeratorsanddenominators = 2 Cancelcommonfactorofnumeratoranddenominator$

Hence, $R (x) = 2 .$

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