Q. 69 In the following exercises, find... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 69 (page 653)

In the following exercises, find $R (x) = \frac{f (x)}{g (x)}$ where $f (x)$ and $g (x)$ are known.
$f (x) = \frac{16 x^{2}}{4 x + 36} g (x) = \frac{4 x^{2} - 24 x}{x^{2} + 4 x - 45}$

Short Answer

Expert verified

The resultant expression is $\frac{x (x - 5)}{(x - 6)}$

Step by step solution

Step 1. Given Information

The given rational expresions are $f (x) = \frac{16 x^{2}}{4 x + 36} g (x) = \frac{4 x^{2} - 24 x}{x^{2} + 4 x - 45}$

Step 2. Rewrite the Expression as a Product

Substitute the given values into $R (x) = \frac{f (x)}{g (x)}$ .
role="math" localid="1644819781853" $R (x) = \frac{\frac{16 x^{2}}{4 x + 36}}{\frac{4 x^{2} - 24 x}{x^{2} + 4 x - 45}}$
Write the obtained expression as the product of numerator and the reciprocal of denominator.
$R (x) = \frac{16 x^{2}}{4 x + 36} 脳 \frac{x^{2} + 4 x - 45}{4 x^{2} - 24 x}$

Step 3. Factor the Numerator and Denomiantor

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

$R (x) = \frac{4 脳 4 脳 x 脳 x}{4 (x + 9)} 脳 \frac{(x + 9) (x - 5)}{4 脳 x 脳 (x - 6)}$

Step 4. Cancel out the Common Factors

Simplify the obtained expression by canceling out the common factors.

$\begin{array}{rcl} R (x) & = & \frac{4 脳 4 脳 x 脳 x}{4 (x + 9)} 脳 \frac{(x + 9) (x - 5)}{4 脳 x 脳 (x - 6)} \\ = & \frac{x (x - 5)}{(x - 6)} \end{array}$

So, the simplified result is $\frac{x (x - 5)}{(x - 6)}$ .

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91影视

In the following exercises, find $R (x) = \frac{f (x)}{g (x)}$ where $f (x)$ and $g (x)$ are known.
$f (x) = \frac{16 x^{2}}{4 x + 36} g (x) = \frac{4 x^{2} - 24 x}{x^{2} + 4 x - 45}$

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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91影视

In the following exercises, find R(x)=f(x)g(x)where f(x)and g(x)are known.fx=16x24x+36gx=4x2-24xx2+4x-45

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

Discrete Mathematics

Geometry

Probability and Statistics

Theoretical and Mathematical Physics

Calculus

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, find $R (x) = \frac{f (x)}{g (x)}$ where $f (x)$ and $g (x)$ are known.
$f (x) = \frac{16 x^{2}}{4 x + 36} g (x) = \frac{4 x^{2} - 24 x}{x^{2} + 4 x - 45}$