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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 61 (page 653)

In the following exercises, find the domain of each function.
$R (x) = \frac{3 x^{2} + 15 x}{6 x^{2} + 6 x - 36}$

Short Answer

Expert verified

The domain is $R - \{- 3, 2\}$

Step by step solution

01

Given Information

$R (x) = \frac{3 x^{2} + 15 x}{6 x^{2} + 6 x - 36}$

02

Step 2. Factor the denominator

Set the denominator zero

$6 x^{2} + 6 x - 36 = 0 6 (x^{2} + x - 6) = 0$

6 (x^{2} + x - 6) = 0 6 (x + 3) (x - 2) = 0

03

Step 3. Use the Zero Product Property

$(x + 3) = 0 o r (x - 2) = 0 x = - 3, 2$

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Most popular questions from this chapter

Simplify the complex rational expression by using the LCD:

$\frac{\frac{1}{a} + \frac{1}{b}}{\frac{a}{b} + \frac{b}{a}}$

Determine the values for which the rational expression is undefined.

$\frac{5 a + 3}{3 a - 2}$

In the following exercises, divide the rational expressions.

$\frac{\frac{3 b^{2} + 2 b - 8}{12 b + 18}}{\frac{3 b^{2} + 2 b - 8}{2 b^{2} - 7 b - 15}}$

In the following exercises, multiply the rational expressions. $\frac{72 m - 12 m^{2}}{8 m + 32} . \frac{m^{2} + 10 m + 24}{m^{2} - 36}$

In the following exercises, divide the rational expressions.

$\frac{\frac{2 a^{2} - a - 21}{5 a + 20}}{\frac{a^{2} + 7 a + 12}{a^{2} + 8 a + 16}}$

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