1
Section 5.1 
Rational Expressions
Definition:
A
rational expression
is a function made from the ratio of two polynomials.
Rational Expressions
Rational expressions are fractions with a polynomial in the numerator and a (probably different)
polynomial in the denominator.
Examples:
1.
The function
2
3
4
ba
ab
is a rational expression.
It is the ratio of two monomials.
2.
The function
9
1
2


y
x
is a rational expression.
It is the ratio of two binomials.
3.
The function
10
11
8
2
2
2
+



x
x
x
x
is a rational expression.
It is the ratio of two trinomials.
4.
The function
1
2
1
2
+


x
x
x
is a rational expression.
It is the ratio of one binomial to one
trinomial.
5.
The function 2
x
4
yz
2
is a rational expression because any polynomial may be written as a
fraction by placing it over 1:
1
2
2
4
yz
x
.
6.
The function
8
2
8
3
2

+
x
x
is not a rational expression because
8
3
+
x
is not a polynomial.
Simplifying Rational Expressions
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 Spring '08
 Staff
 Polynomials, Rational Expressions, Fractions, Fraction, Rational function, rational expression

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