Beginning Algebra, 11th Edition

420 CHAPTER 7 Rational Expressions and Applications

OBJECTIVES The quotient of two integers (with denominator not 0), such as or is called a

rational number.In the same way, the quotient of two polynomials with denominator

not equal to 0 is called a rational expression.

(^23) - (^34) ,
The Fundamental Property of Rational Expressions
7.1
1 Find the numerical
value of a rational
expression.
2 Find the values of
the variable for
which a rational
expression is
undefined.
3 Write rational
expressions in
lowest terms.
4 Recognize
equivalent forms of
rational expressions.
Rational Expression
A rational expressionis an expression of the form where Pand Qare poly-
nomials and Q Z0.
P
Q^ ,
and Rational expressions
Our work with rational expressions requires much of what we learned in Chapters 5
and 6on polynomials and factoring, as well as the rules for fractions from Section 1.1.
OBJECTIVE 1 Find the numerical value of a rational expression.We use
substitution to evaluate a rational expression for a given value of the variable.
Evaluating Rational Expressions
Find the numerical value of for the given value of x.
(a)
Let
Simplify.
a

• b=-
  a
  =- b

9

2

=

9

- 2

= x=1.

3112 + 6

2112 - 4

3 x+ 6

2 x- 4

x= 1

3 x+ 6

2 x- 4

EXAMPLE 1

2 m^3

8

9 x

y+ 3

,

• 6 x
  x^3 + 8

,

(b)

Let

Simplify.

0

= (^0) b= 0

=

0

- 8

= x=-2.

31 - 22 + 6

21 - 22 - 4

3 x+ 6

2 x- 4

x=- 2

OBJECTIVE 2 Find the values of the variable for which a rational expres-

sion is undefined.In the definition of a rational expression Qcannot equal 0.

The denominator of a rational expression cannot equal 0 because division by 0 is

undefined.

For instance, in the rational expression

Denominator cannot equal 0.

3 x+ 6

2 x- 4

P

Q^ ,

from Example 1,the variable xcan take on any real number value except 2. If xis 2,

then the denominator becomes making the expression undefined.

Thus, xcannot equal 2. We indicate this restriction by writing xZ2.

2122 - 4 = 0 ,

NOW TRY
EXERCISE 1
Find the value of the follow-
ing rational expression for

2 x- 1

x+ 4

x=-3.

NOW TRY ANSWER

1. 
   
   
   
   • 7
   
   
   
   

Use parentheses

around negative

numbers to avoid

errors.

NOW TRY

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