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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 4 (page 651)

In the following exercises, determine the values for which the rational expression is defined.
$(a) \frac{5 p q^{2}}{9 q} (b) \frac{7 a - 4}{3 a + 5} (c) \frac{1}{x^{2} - 4}$

Short Answer

Expert verified

$(a) \frac{5 p q^{2}}{9 q} undefinendat q = 0 (b) \frac{7 a - 4}{3 a + 5} undefinedat a = - \frac{5}{3} (c) \frac{1}{x^{2} - 4} undefinedat x = - 2, 2 .$

Step by step solution

01

Step 1.Given information

$(a) \frac{5 p q^{2}}{9 q} (b) \frac{7 a - 4}{3 a + 5} (c) \frac{1}{x^{2} - 4}$

02

Part a.step 1.find the undefined values

$(a) \frac{5 p q^{2}}{9 q}$

Equate the denominator to zero and solve for the unknown variable.

$9 q = 0 q = 0$

Hence, the undefined value at $q = 0 .$

03

Part b.step 1.find the undefined values

$(b) \frac{7 a - 4}{3 a + 5}$

Equate the denominator to zero and solve for the unknown variable.

$3 a + 5 = 0 3 a = - 5 a = - \frac{5}{3}$

Hence, the undefined value at $a = - \frac{5}{3} .$

04

Part c.step 1.find the undefined values

$(c) \frac{1}{x^{2} - 4}$

Equate the denominator to zero and solve for the unknown variable.

$x^{2} - 4 = 0 x^{2} = 4 x = 卤 2$

Hence, the undefined value at $x = - 2, 2 .$

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Most popular questions from this chapter

In the following exercises, divide the rational expressions.

$\frac{3 s^{2}}{s^{2} - 16} 梅 \frac{s^{3} - 4 s^{2} + 16 s}{s^{3} - 64}$

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