Chapter 7: Q. 7.46 (page 666)

Find $R (x) = f (x) + g (x)$ where $f (x) = \frac{x - 4}{x + 3}$ and $g (x) = \frac{4 x + 6}{x^{2} - 9}$ .

Short Answer

Expert verified

The resultant expression is $\frac{x^{2} - 3 x + 18}{(x - 3) (x + 3)}$ .

Step by step solution

Step 1. Given Information

The given functions are $f (x) = \frac{x - 4}{x + 3}, g (x) = \frac{4 x + 6}{x^{2} - 9}$ .

Step 2. Determine the expression

Substitute the given functions into $R (x) = f (x) + g (x)$ .

$R (x) = \frac{x - 4}{x + 3} + \frac{4 x + 6}{x^{2} - 9}$

Step 3. Express with common denominator

Factor the denominators of the obtained expression.

$\frac{x - 4}{x + 3} + \frac{4 x + 6}{(x - 3) (x + 3)}$

The LCD of the terms of obtained expression is $(x - 3) (x + 3)$ .
Multiply the numerator and denominator of first term by $(x - 3)$ .

$\begin{array}{rcl} \frac{(x - 4) (x - 3)}{(x + 3) (x - 3)} + \frac{4 x + 6}{(x - 3) (x + 3)} & = & \frac{x^{2} - 4 x - 3 x + 12}{(x + 3) (x - 3)} + \frac{4 x + 6}{(x - 3) (x + 3)} \\ = & \frac{x^{2} - 7 x + 12}{(x + 3) (x - 3)} + \frac{4 x + 6}{(x - 3) (x + 3)} \end{array}$

Step 4. Simplify

As the denominator is the same for both the terms, perform addition in the numerator and place it over the common denominator.

$\begin{array}{rcl} \frac{x^{2} - 7 x + 12 + 4 x + 6}{(x + 3) (x - 3)} \end{array} = \begin{array}{rcl} \frac{x^{2} - 3 x + 18}{(x + 3) (x - 3)} \end{array}$

So, the resultant expression is $\begin{array}{rcl} \frac{x^{2} - 3 x + 18}{(x + 3) (x - 3)} \end{array}$ .

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Find $R (x) = f (x) + g (x)$ where $f (x) = \frac{x - 4}{x + 3}$ and $g (x) = \frac{4 x + 6}{x^{2} - 9}$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Determine the expression

Step 3. Express with common denominator

Step 4. Simplify

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FindR(x)=f(x)+g(x)wheref(x)=x-4x+3andg(x)=4x+6x2-9.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Determine the expression

Step 3. Express with common denominator

Step 4. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Decision Maths

Mechanics Maths

Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

Find $R (x) = f (x) + g (x)$ where $f (x) = \frac{x - 4}{x + 3}$ and $g (x) = \frac{4 x + 6}{x^{2} - 9}$ .