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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. 423 (page 736)

In the following exercise, find $R (x) = f (x) + g (x)$ where $f (x)$ and $g (x)$ are given role="math" localid="1646707453949" $f (x) = \frac{2 x^{2} + 12 x - 11}{x^{2} + 3 x - 10}$ ,role="math" localid="1646707470103" $g (x) = \frac{x + 1}{2 - x}$

Short Answer

Expert verified

The solution is $\frac{x + 8}{x + 5}$

Step by step solution

01

Step 1. Given Information

$f (x) = \frac{2 x^{2} + 12 x - 11}{x^{2} + 3 x - 10}$ and $g (x) = \frac{x + 1}{2 - x}$

02

Step 2. Find Rx=fx+gx

The LCD of $x^{2} + 3 x - 10, 2 - x : (x - 2) (x + 5) (- x + 2)$

Rewrite each rational expression as an equivalent rational expression with LCD.

$R (x) = f (x) + g (x) R (x) = \frac{(2 x^{2} + 12 x - 11) (- x + 2)}{(x - 2) (x + 5) (- x + 2)} + \frac{- (x + 1) (x + 5) (- x + 2)}{(x - 2) (x + 5) (- x + 2)} R (x) = \frac{(2 x^{2} + 12 x - 11) (- x + 2) - (x + 1) (x + 5) (- x + 2)}{(x - 2) (x + 5) (- x + 2)} R (x) = \frac{x + 8}{x + 5}$

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Most popular questions from this chapter

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