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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. 7.1 (page 641)

Determine the value for which each rational expression is undefined.
$(a) \frac{3 y^{2}}{8 x} (b) \frac{8 n - 5}{3 n + 1} (c) \frac{a + 10}{a^{2} + 4 a + 3}$

Short Answer

Expert verified

$(a) \frac{3 y^{2}}{8 x}$ is undefined at $x = 0 .$

$(b) \frac{8 n - 5}{3 n + 1}$ is undefined at $n = - \frac{1}{3} .$

$(c) \frac{a + 10}{a^{2} + 4 a + 3}$ is undefined at

$a = - 3 or a = - 1$

Step by step solution

01

Step 1. Given information

The given rational expressions are

(a) \frac{3 y^{2}}{8 x} (b) \frac{8 n - 5}{3 n + 1} (c) \frac{a + 10}{a^{2} + 4 a + 3}

02

Part a. Step 1. Find the undefined values

$(a) \frac{3 y^{2}}{8 x}$

Set the denominator equal to zero and solve the equation

$8 x = 0$

$x = 0$

Hence, the given rational expression is undefined at $x = 0 .$

03

Part b. Step 1.Find the undefined values

$(b) \frac{8 n - 5}{3 n + 1}$

Set the denominator equal to zero and solve the equation

$3 n + 1 = 0 3 n = - 1 n = - \frac{1}{3}$

Hence, the given rational expression is undefined atlocalid="1644829474496" $n = - \frac{1}{3} .$

04

Part c. Step1. Find the undefined values

$(c) \frac{a + 10}{a^{2} + 4 a + 3}$

Set the denominator equal to zero and solve the equation

$a^{2} + 4 a + 3 = 0 a^{2} + 3 a + a + 3 = 0 a (a + 3) + (a + 3) = 0 (a + 3) (a + 1) = 0 (a + 3) = 0 or (a + 1) = 0 a = - 3 or a = - 1$

Hence, the given rational expression is undefined at $a = - 3 or a = - 1 .$

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