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MA 152
Lesson 9
Section P.6
I
Rational Expressions
If
x
and
y
are real numbers (
0
≠
y
), the quotient
y
x
is called a fraction or
rational
expression.
Ex 1:
Evaluate the following rational expression if
x
= 12
2
4
3
1
2 (
5)
x
x
x x

+

Remember, a fraction (or rational expression) cannot have a zero denominator.
(Division
by zero is undefined.)
If a denominator has a variable, that variable cannot be any value
that makes the denominator equal zero.
The set of numbers for which a rational
expression would be
defined
is called the
domain.
Any value of the variable which
makes a denominator equal zero
must be excluded from the domain.
For example, the
domain of the following rational expression would exclude
2 and 4

, since those
numbers make a factor of the denominator equal zero.
2
2
1
2
1
2
8
(
4)(
2)
4
0
2
0
4
2
x
x
x
x
x
x
x
x
x
x
+
+
=



+
 ≠
+ ≠
≠
≠ 
The domain of this expression excludes
2 and 4

.
Ex 2:
Find any numbers that would be excluded from the domain of each rational
expression.
2
3
)
3
a
x
x
+
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2
2
2
)
5
6
5
2
)
4
1
x
b
x
x
x
c
x
+
+
+
+

II
Simplifying Rational Expression
1.
Factor the numerator and denominator completely.
2.
Divide both numerator and denominator by any common factors.
*Note:
Determine what values would be excluded from the domain prior to dividing
out any common factors.
Ex 3:
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 Fall '09
 Staff
 Rational Expressions, Real Numbers

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