Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 6 - Section 6.1 - Rational Functions and Multiplying and Dividing Rational Expressions - Vocabulary, Readiness & Video Check - Page 345: 9

Answer

The denominators of rational expressions cannot be zero as division of zero is not allowed.

Work Step by Step

RECALL: A rational expression involves a variable in the denominator. The denominator of a rational expression cannot be zero as it means that you are dividing 0 to the numerator. Dividing zero to any number is not allowed as it makes the expression undefined. The values of the variable that make the denominator zero are the numbers that are excluded in the domain of the rational function. Example: In the rational function $f(x)=\dfrac{1}{x-2}$, the value of $x$ cannot be $2$ as it makes the denominator equal to zero. This is the reason why the domain of this function is any real number except 2.
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