Chapter 11: Q144E. (page 1069)

In the following exercise, find
(a) $R (x) = f (x) + g (x)$
(b) $R (x) = f (x) - g (x)$ :
$f (x) = \frac{- 4 x - 24}{x^{2} + x - 30} g (x) = \frac{x + 7}{5 - x}$

Short Answer

Expert verified

(a) $R (x) = \frac{- x - 11}{x - 5}$

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

Step by step solution

Step 1. Given information.

The following information is given:

$f (x) = \frac{- 4 x - 24}{x^{2} + x - 30} g (x) = \frac{x + 7}{5 - x}$

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

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

Substituting the values

$R (x) = \frac{- 4 x - 24}{x^{2} + x - 30} + \frac{x + 7}{5 - x}$

Factorise the denominators:

$R (x) = \frac{- 4 x - 24}{(x + 6) (x - 5)} + \frac{x + 7}{5 - x}$

Multiply the numerator and the denominator of the second term by $- 1$ and then simplify:

$R (x) = \frac{- 4 x - 24}{(x + 6) (x - 5)} + \frac{(- 1) (x + 7)}{(- 1) (5 - x)} R (x) = \frac{- 4 (x + 6)}{(x + 6) (x - 5)} - \frac{(x + 7)}{(x - 5)}$

Cancel the common factors from the numerator and the denominator:

$R (x) = \frac{- 4}{(x - 5)} - \frac{(x + 7)}{(x - 5)}$

Since common LCD is present, simplify:

$R (x) = \frac{- 4 - x - 7}{(x - 5)} R (x) = \frac{- x - 11}{x - 5}$

Step 3. Find out (b) Rx=f(x)-g(x)

By factorising the terms,

$R (x) = \frac{- 4 (x + 6)}{(x + 6) (x - 5)} - \frac{x + 7}{5 - x}$

Cancelling $x + 6$ from the first term and multiplying both the numerator and the denominator of the second term by $- 1$ and then simplifying:

localid="1644743911735" $R (x) = \frac{- 4}{(x - 5)} - \frac{(- 1) (x + 7)}{(- 1) (5 - x)} R (x) = \frac{- 4}{(x - 5)} + \frac{(x + 7)}{(x - 5)}$

Simplify:

$R (x) = \frac{- 4 + x + 7}{(x - 5)} R (x) = \frac{x + 3}{x - 5}$

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In the following exercise, find
(a) $R (x) = f (x) + g (x)$
(b) $R (x) = f (x) - g (x)$ :
$f (x) = \frac{- 4 x - 24}{x^{2} + x - 30} g (x) = \frac{x + 7}{5 - x}$

Short Answer

Step by step solution

Step 1. Given information.

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

Step 3. Find out (b) Rx=f(x)-g(x)

One App. One Place for Learning.

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In the following exercise, find(a) Rx=fx+gx(b) Rx=fx-gx:fx=-4x-24x2+x-30gx=x+75-x

Short Answer

Step by step solution

Step 1. Given information.

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

Step 3. Find out (b) Rx=f(x)-g(x)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

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Study anywhere. Anytime. Across all devices.

In the following exercise, find
(a) $R (x) = f (x) + g (x)$
(b) $R (x) = f (x) - g (x)$ :
$f (x) = \frac{- 4 x - 24}{x^{2} + x - 30} g (x) = \frac{x + 7}{5 - x}$