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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. 7.22 (page 649)

Find $R (x) = f (x) 路 g (x)$ where $f (x) = \frac{x^{2} - x}{3 x^{2} + 27 x - 30}$ and $g (x) = \frac{x^{2} - 100}{x^{2} - 10 x} .$

Short Answer

Expert verified

The value of $R (x) = \frac{1}{3} .$

Step by step solution

01

Step 1. Given information

$f (x) = \frac{x^{2} - x}{3 x^{2} + 27 x - 30}, g (x) = \frac{x^{2} - 100}{x^{2} - 10 x} R (x) = f (x) 路 g (x)$

02

Step 2. Find R(x)

$R (x) = f (x) 路 g (x) R (x) = \frac{x^{2} - x}{3 x^{2} + 27 x - 30} 路 \frac{x^{2} - 100}{x^{2} - 10 x} Usegivendata = \frac{x (x - 1)}{3 (x + 10) (x - 1)} 路 \frac{(x - 10) (x + 10)}{x (x - 10)} Factorize = \frac{x (x - 1) (x - 10) (x + 10)}{3 x (x + 10) (x - 1) (x - 10)} Multiplythe numerator and denominator = \frac{1}{3} Cancelcommonfactorofnumeratoranddenominator$

Hence, $R (x) = \frac{1}{3} .$

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