copyright © 2010 pearson education, inc. all rights reserved sec 8.1 - 1 rational expressions and...
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Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 8.1 - 1
Rational Expressions and Functions
Chapter 8
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Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 2
8.1 Rational Expressions and Functions; Multiplying and Dividing
Defining Rational Expressions
In Section 1.1, we defined rational numbers to be the quotient of two integers, a / b with b not equal to 0.
A rational expression (algebraic fraction) is the quotient of two polynomials, also with the denominator not 0. Rational expressions are the elements of the set
Examples:
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Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 3
8.1 Rational Expressions and Functions; Multiplying and Dividing
Define Rational Functions and Describe Their Domain
A rational function has the form
The domain of a rational function includes all the real numbers except those that make Q(x), the denominator, equal to 0.
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Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 4
8.1 Rational Expressions and Functions; Multiplying and Dividing
Writing Rational Expressions in Lowest Terms
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Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 5
8.1 Rational Expressions and Functions; Multiplying and Dividing
Writing Rational Expressions in Lowest Terms
3
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Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 6
8.1 Rational Expressions and Functions; Multiplying and Dividing
Multiplying Rational Expressions
3
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Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 7
8.1 Rational Expressions and Functions; Multiplying and Dividing
Finding the Reciprocal of a Rational Expression
3To find the reciprocal, simply interchange the numerator and denominator.
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Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 8.1 - 8
8.1 Rational Expressions and Functions; Multiplying and Dividing
Dividing Rational Expressions
3