## Introductory Algebra for College Students (7th Edition)

Published by Pearson

# Chapter 7 - Section 7.1 - Rational Expressions and Their Simplification - Exercise Set - Page 491: 10

#### Answer

$x=4\frac{3}{4}$ or $x=-2$

#### Work Step by Step

A rational expression is undefined when the value of its denominator is zero. Write and solve an expression where the denominator is zero. $(4x-19)(x+2)=0$ A product is zero when either factor is zero. $4x-19=0$ or $x+2=0$ Use the addition property of equality to solve both equations for x. $4x-19+19=0+19$ or $x+2-2=0-2$ Simplify. $4x=19$ or $x=-2$ Use the multiplication property of equality to solve the first equation for x. $4x\div4=19\div3$ or $x=-2$ Simplify. $x=4\frac{3}{4}$ or $x=-2$

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