Chapter 4: Q. 45 (page 246)

Solve each inequality. Graph the solution set.
$\frac{x^{2} - 8 x + 12}{x^{2} - 16} > 0$

Short Answer

Expert verified

The real zeroes of the function are 6, 2 , 4 and $- 4$ and the graph is

Step by step solution

Step 1. Given Information

The given inequality is $\frac{x^{2} - 8 x + 12}{x^{2} - 16} > 0$

Step 2. Calculation

The inequality is already in a form with zero on the right side.

Solve the given inequality by finding the real zeroes of the numerator and denominator.

$x^{2} - 8 x + 12 = 0 (x - 6) (x - 2) = 0 x = 6, 2$

And

$x^{2} - 16 = 0 x^{2} = 16 x = \pm 4$

Thus, real zeroes of the function are 6, 2, 4 and $- 4$

Step 3. Graph

Construct the table by using a number from each interval to check whether the function is positive or negative.

Thus, the solution set is $\{x | x < - 4 o r 2 < x < 4 o r x > 6\}$

And the solution set can be graphed as

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Solve each inequality. Graph the solution set.
$\frac{x^{2} - 8 x + 12}{x^{2} - 16} > 0$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

Step 3. Graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Applied Mathematics

Mechanics Maths

Pure Maths

Calculus

Study anywhere. Anytime. Across all devices.

Solve each inequality. Graph the solution set.x2-8x+12x2-16>0

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

Step 3. Graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Applied Mathematics

Mechanics Maths

Pure Maths

Calculus

Study anywhere. Anytime. Across all devices.

Solve each inequality. Graph the solution set.
$\frac{x^{2} - 8 x + 12}{x^{2} - 16} > 0$