Carson Elementary And Intermediate Algebra 3e
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4M098
Carson Elementary and Intermediate Algebra 3e
Section 7.1
Objectives
1.
Evaluate rational expressions
2.
Find numbers that cause a rational expression to be undefined.
3.
Simplify rational expressions containing only monomials.
4.
Simplify rational expressions containing multiterm polynomials.
Vocabulary
Rational expression
P
An expression that can be written in the form
, where P and Q are polynomials and
Q
Q ≠ 0.
Prior Knowledge
Rational numbers are numbers that can be expressed in the form a/b where a and b are integers and b≠0.
Fractions are undefined if the denominator equals 0.
To evaluate means to replace the variable(s) with the given value(s).
New Concepts
1. Evaluate rational expressions.
This chapter deals with rational expressions and rational equations. The word association for rational is
fraction. We’ll spend some time reviewing our basic fraction arithmetic skills. We use exactly the same
process with rational expressions (algebraic fractions) as we do with arithmetic fractions - the problems
are just a little uglier looking!!!
To evaluate a rational expression, replace the variable(s) with the given values.
3
x
2
Example 1: Evaluate
when x = 2.
4
x
5
Replace the variable with the given number.
( 3
) 2
2
( 4
) 2
5
6
2
8
5
Evaluate the numerator and the denominator.
8
3
4
x
Example 2: Evaluate
when x = 3.
x
3
Replace the variable with the given number.
( 4
) 3
(
) 3
3
Evaluate the numerator and the denominator. This
12
expression is undefined.
0
V. Zabrocki 2011
page 1
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