Chapter 7: Q. 64 (page 653)

For the following exercises, find $R (x) = f (x) g (x)$ where $f (x) a n d g (x)$ are given.
$f (x) = \frac{x^{2} - 2 x}{x^{2} + 6 x - 16} a n d g (x) = \frac{x^{2} - 64}{x^{2} - 8 x}$

Short Answer

Expert verified

The value of $R (x) = 1$

Step by step solution

Step 1. Given Information

$f (x) = \frac{x^{2} - 2 x}{x^{2} + 6 x - 16} a n d g (x) = \frac{x^{2} - 64}{x^{2} - 8 x}$

Step 2. Factor each numerator and denominator

$R (x) = \frac{x^{2} - 2 x}{x^{2} + 6 x - 16} . \frac{x^{2} - 64}{x^{2} - 8 x} R (x) = \frac{x (x - 2)}{(x + 8) (x - 2)} . \frac{(x - 8) (x + 8)}{x (x - 8)}$

Step 3. Remove common factors and simplify

$R (x) = \frac{x (x - 2) (x - 8) (x + 8)}{x (x - 8) (x + 8) (x - 2)} R (x) = 1$

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For the following exercises, find $R (x) = f (x) g (x)$ where $f (x) a n d g (x)$ are given.
$f (x) = \frac{x^{2} - 2 x}{x^{2} + 6 x - 16} a n d g (x) = \frac{x^{2} - 64}{x^{2} - 8 x}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factor each numerator and denominator

Step 3. Remove common factors and simplify

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For the following exercises, find Rx=fxgxwhere fxandgxare given.fx=x2-2xx2+6x-16andgx=x2-64x2-8x

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factor each numerator and denominator

Step 3. Remove common factors and simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Applied Mathematics

Statistics

Decision Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

For the following exercises, find $R (x) = f (x) g (x)$ where $f (x) a n d g (x)$ are given.
$f (x) = \frac{x^{2} - 2 x}{x^{2} + 6 x - 16} a n d g (x) = \frac{x^{2} - 64}{x^{2} - 8 x}$