Chapter 7: Q. 67 (page 653)

For the following exercises, find $R (x) = \frac{f (x)}{g (x)}$ where $f (x)$ and $g (x)$ are given.
localid="1644858875634" $f (x) = \frac{27 x^{2}}{3 x - 21} g (x) = \frac{3 x^{2} + 18 x}{x^{2} + 13 x + 42}$

Short Answer

Expert verified

The resultant expression is $\frac{3 x (x + 7)}{(x - 7)}$ .

Step by step solution

Step 1. Given information

The given rational expressions are $f (x) = \frac{27 x^{2}}{3 x - 21} g (x) = \frac{3 x^{2} + 18 x}{x^{2} + 13 x + 42}$

Step 2. Rewrite the Expression as a Product

Substitute the given values into $R (x) = \frac{f (x)}{g (x)}$ .

role="math" localid="1644817631746" $R (x) = \frac{\frac{27 x^{2}}{3 x - 21}}{\frac{3 x^{2} + 18 x}{x^{2} + 13 x + 42}}$

Write the obtained epression as the product of numerator and the reciprocal of denominator.

$R (x) = \frac{27 x^{2}}{3 x - 21} \times \frac{x^{2} + 13 x + 42}{3 x^{2} + 18 x}$

Step 3. Factor the Numerator and Denomiantor

Express the numerator and denominator of the obtained expression as factors.

$R (x) = \frac{3 \times 3 \times 3 \times x \times x}{3 (x - 7)} \times \frac{(x + 6) (x + 7)}{3 x (x + 6)}$

Step 4. Cancel out the Common Factors

Simplify the obtained expression by canceling out the common factors.

$\begin{array}{rcl} R (x) & = & \frac{3 \times 3 \times 3 \times x \times x}{3 (x - 7)} \times \frac{(x + 6) (x + 7)}{3 x (x + 6)} \\ = & \frac{3 x (x + 7)}{(x - 7)} \end{array}$

So, the simplified result is $R (x) = \frac{3 x (x + 7)}{(x - 7)}$ .

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For the following exercises, find $R (x) = \frac{f (x)}{g (x)}$ where $f (x)$ and $g (x)$ are given.
localid="1644858875634" $f (x) = \frac{27 x^{2}}{3 x - 21} g (x) = \frac{3 x^{2} + 18 x}{x^{2} + 13 x + 42}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Rewrite the Expression as a Product

Step 3. Factor the Numerator and Denomiantor

Step 4. Cancel out the Common Factors

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For the following exercises, find R(x)=f(x)g(x)where f(x)and g(x)are given.localid="1644858875634" fx=27x23x-21gx=3x2+18xx2+13x+42

Short Answer

Step by step solution

Step 1. Given information

Step 2. Rewrite the Expression as a Product

Step 3. Factor the Numerator and Denomiantor

Step 4. Cancel out the Common Factors

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Applied Mathematics

Geometry

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

For the following exercises, find $R (x) = \frac{f (x)}{g (x)}$ where $f (x)$ and $g (x)$ are given.
localid="1644858875634" $f (x) = \frac{27 x^{2}}{3 x - 21} g (x) = \frac{3 x^{2} + 18 x}{x^{2} + 13 x + 42}$