Chapter 7: Q. 368 (page 732)

In the following exercises, solve each rational inequality and write the solution in interval notation.
$\frac{4}{x^{2} - 25} > 0$

Short Answer

Expert verified

Solution for rational inequality is $x \in (- \infty, - 5) \cup (5, \infty) .$

Step by step solution

Step 1. Given Information

Given that the rational inequality is $\frac{4}{x^{2} - 25} > 0 .$

Step 2. Polynomial factor

On factoring the polynomial,

$f (x) = \frac{4}{x^{2} - 25} f (x) = \frac{4}{x^{2} - 5^{2}} f (x) = \frac{4}{(x - 5) (x + 5)}$

Step 3. Critical point

To find the critical points,

$(x - 5) = 0 x = 5 (x + 5) = 0 x = - 5$

There is an undefined polynomial function at this critical points. It will not be included. On dividing the number line,

To test the polynomial expression sign, it indicates the number line sign.

$\frac{1}{x^{2} - 16} < 0, (- \infty, - 5) \cup (5, \infty) f (x) < 0, x \in (- \infty, - 5) \cup (5, \infty)$

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In the following exercises, solve each rational inequality and write the solution in interval notation.
$\frac{4}{x^{2} - 25} > 0$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Polynomial factor

Step 3. Critical point

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In the following exercises, solve each rational inequality and write the solution in interval notation.4x2-25>0

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Polynomial factor

Step 3. Critical point

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Statistics

Decision Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each rational inequality and write the solution in interval notation.
$\frac{4}{x^{2} - 25} > 0$