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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. 7.2 (page 641)

Determine the value for which each rational expression is undefined.
$(a) \frac{4 p}{5 q} (b) \frac{y - 1}{3 y + 2} (c) \frac{m - 5}{m^{2} + m - 6}$

Short Answer

Expert verified

$(a) \frac{4 p}{5 q}$ is undefined at $q = 0 .$

$(b) \frac{y - 1}{3 y + 2}$ is defined at $y = - \frac{2}{3}$ .

$(c) \frac{m - 5}{m^{2} + m - 6}$ is undefined at $m = - 3 or m = 2$

Step by step solution

01

Step 1. Given information

The given rational expressions are

(a) \frac{4 p}{5 q} (b) \frac{y - 1}{3 y + 2} (c) \frac{m - 5}{m^{2} + m - 6}

02

Part a. Step 1.Find the undefined values

$(a) \frac{4 p}{5 q}$

Set the denominator equal to zero and solve the equation

$5 q = 0 鈬� q = 0$

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

03

Part b. Step 2.Find the undefined values

$(b) \frac{y - 1}{3 y + 2}$

Set the denominator equal to zero and solve the equation

$3 y + 2 = 0 3 y = - 2 y = - \frac{2}{3}$

Hence, the given rational expression is undefined at $y = - \frac{2}{3} .$

04

Part c. Step 1.Find the undefined values

$(c) \frac{m - 5}{m^{2} + m - 6}$

Set the denominator equal to zero and solve the equation

$m^{2} + m - 6 = 0 m^{2} + 3 m - 2 m - 6 = 0 m (m + 3) - 2 (m + 3) = 0 (m + 3) (m - 2) = 0 m + 3 = 0 or m - 2 = 0 m = - 3 or m = 2$

Hence, the given rational expression is undefined at $m = - 3 or m = 2 .$

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Most popular questions from this chapter

Simplify the complex rational expression by writing it as a division:

$\frac{\frac{1}{2} + \frac{2}{3}}{\frac{5}{6} + \frac{1}{12}}$

Simplify the complex rational expression by LCD:

$\frac{\frac{1}{2} + \frac{1}{5}}{\frac{1}{10} + \frac{1}{5}}$

For the following exercises, perform the indicated operations.

$\frac{4 n^{2} + 32 n}{3 n + 2} . \frac{3 n^{2} - n - 2}{n^{2} + n - 30} 梅 \frac{108 n^{2} - 24 n}{n + 6}$

In the following exercise, perform the indicated operation:

$\frac{2 b}{b - 5} + \frac{3}{2 b} - \frac{2 b - 15}{2 b^{2} - 10 b}$

Solve the equation $c = \frac{2}{a} + \frac{b}{5}$ for the variable $a$ .

See all solutions

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