Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q146E. (page 669)

In the following exercise, find
(a) $R (x) = f (x) + g (x)$
(b) $R (x) = f (x) - g (x)$ :
role="math" localid="1644749808906" $f (x) = \frac{5}{x + 7} g (x) = \frac{10 x}{x^{2} - 49}$

Short Answer

Expert verified

(a) $R (x) = \frac{5 (3 x - 7)}{(x + 7) (x - 7)}$

(b) $R (x) = \frac{- 5}{(x - 7)}$

Step by step solution

Step 1. Given information.

The following information is given:

$f (x) = \frac{5}{x + 7} g (x) = \frac{10 x}{x^{2} - 49}$

Step 2. Finding (a) Rx=fx+gx

$R (x) = f (x) + g (x)$

Substituting the values

role="math" localid="1644749830492" $R (x) = \frac{5}{x + 7} + \frac{10 x}{x^{2} - 49}$

Factor the denominator:

role="math" localid="1644749841956" $R (x) = \frac{5}{x + 7} + \frac{10 x}{(x - 7) (x + 7)}$

Find out the LCD:

$(x - 7) (x + 7)$

Rewrite the expression with the denominator equal to the LCD:

$R (x) = \frac{5 (x - 7)}{(x + 7) (x - 7)} + \frac{10 x}{(x - 7) (x + 7)}$

Simplify:

$R (x) = \frac{5 x - 35 + 10 x}{(x + 7) (x - 7)} R (x) = \frac{15 x - 35}{(x + 7) (x - 7)} R (x) = \frac{5 (3 x - 7)}{(x + 7) (x - 7)}$

Step 3. Finding (b) Rx=fx-gx

$R (x) = f (x) - g (x)$

Substituting the values (after the denominator factored and made equal to LCD):

$R (x) = \frac{5 (x - 7)}{(x - 7) (x + 7)} - \frac{10 x}{(x - 7) (x + 7)}$

Simplify:

$R (x) = \frac{5 x - 35 - 10 x}{(x - 7) (x + 7)} R (x) = \frac{- 5 (x + 7)}{(x - 7) (x + 7)}$

Cancelling common factors from the numerator and the denominator:

$R (x) = \frac{- 5}{(x - 7)}$

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91影视

In the following exercise, find
(a) $R (x) = f (x) + g (x)$
(b) $R (x) = f (x) - g (x)$ :
role="math" localid="1644749808906" $f (x) = \frac{5}{x + 7} g (x) = \frac{10 x}{x^{2} - 49}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Finding (a) Rx=fx+gx

Step 3. Finding (b) Rx=fx-gx

One App. One Place for Learning.

Most popular questions from this chapter

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91影视

In the following exercise, find(a) R(x)=f(x)+g(x)(b) R(x)=f(x)-g(x):role="math" localid="1644749808906" f(x)=5x+7g(x)=10xx2-49

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Finding (a) Rx=fx+gx

Step 3. Finding (b) Rx=fx-gx

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

Discrete Mathematics

Geometry

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercise, find
(a) $R (x) = f (x) + g (x)$
(b) $R (x) = f (x) - g (x)$ :
role="math" localid="1644749808906" $f (x) = \frac{5}{x + 7} g (x) = \frac{10 x}{x^{2} - 49}$