Q. 37 Solve each inequality algebraica... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 4: Q. 37 (page 242)

Solve each inequality algebraically.
$\frac{{(x - 2)}^{2}}{x^{2} - 1} 鈮� 0$

Short Answer

Expert verified

Solution to the inequality $\frac{{(x - 2)}^{2}}{x^{2} - 1} 鈮� 0$ is $(- 鈭�, - 1) 鈭� (1, 鈭�)$ .

Step by step solution

Step 1. Given information

We have been given an inequality $\frac{{(x - 2)}^{2}}{x^{2} - 1} 鈮� 0$ .

We have to solve this inequality algebraically.

Step 2. Determine the real numbers at which the expression f equals zero and at which the expression f is undefined.

Assume $f (x) = \frac{{(x - 2)}^{2}}{x^{2} - 1}$ .

role="math" localid="1646125606350" ${(x - 2)}^{2} = 0 x = 2$

and

$x^{2} - 1 = 0 (x + 1) (x - 1) = 0 x = - 1, 1$

Step 3. Form the intervals

Using the values of x found in previous step, we can divide the real numbers in the intervals:

$(- 鈭�, - 1) 鈭� (- 1, 1) 鈭� (1, 鈭�)$

Step 4. Select a number in each interval and evaluate f at the number

Create the following table:

Interval	$(- 鈭� - 1)$	$(- 1, 1)$	$(1, 鈭�)$
Number chosen	$- 2$	0	$2$
Value of f	$f (- 2) = \frac{16}{3}$	$f (0) = - 4$	$f (2) = 0$
Conclusion	positive	negative	zero

Step 5. Identify the interval

Since we want to know where f is positive or zero, we conclude that $f (x) 鈮� 0$ in the interval $(- 鈭�, - 1) 鈭� (1, 鈭�)$ .

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91影视

Solve each inequality algebraically.
$\frac{{(x - 2)}^{2}}{x^{2} - 1} 鈮� 0$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Determine the real numbers at which the expression f equals zero and at which the expression f is undefined.

Step 3. Form the intervals

Step 4. Select a number in each interval and evaluate f at the number

Step 5. Identify the interval

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91影视

Solve each inequality algebraically. (x-2)2x2-1鈮�0

Short Answer

Step by step solution

Step 1. Given information

Step 2. Determine the real numbers at which the expression f equals zero and at which the expression f is undefined.

Step 3. Form the intervals

Step 4. Select a number in each interval and evaluate f at the number

Step 5. Identify the interval

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

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Study anywhere. Anytime. Across all devices.

Solve each inequality algebraically.
$\frac{{(x - 2)}^{2}}{x^{2} - 1} 鈮� 0$