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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. 424 (page 736)

In the following exercise find $R (x) = f (x) + g (x)$ where $f (x)$ and $g (x)$ are given.role="math" localid="1646708502126" $f (x) = \frac{- 4 x + 31}{x^{2} + x - 30}$ ,role="math" localid="1646708518656" $g (x) = \frac{5}{x + 6}$

Short Answer

Expert verified

The solution is $\frac{1}{x - 5}$

Step by step solution

01

Step 1. Given information

$f (x) = \frac{- 4 x + 31}{x^{2} + x - 30}$ and $g (x) = \frac{5}{x + 6}$

02

Step 2. Find Rx=fx+gx

The LCD of $x^{2} + x - 30, x + 6 : (x - 5) (x + 6)$

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

$R (x) = f (x) + g (x) R (x) = \frac{- 4 x + 31}{(x - 5) (x + 6)} + \frac{5 (x - 5)}{(x - 5) (x + 6)} R (x) = \frac{- 4 x + 31 + 5 (x - 5)}{(x - 5) (x + 6)} R (x) = \frac{1}{x - 5}$

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