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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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.

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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

Probability and Statistics

Pure Maths

Geometry

Statistics

Discrete Mathematics

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