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139

13 Rational Expressions

In this chapter, you apply your skills in factoring polynomials to the charge

of simplifying rational expressions. A rational expression is an algebraic

fraction that has a polynomial for its numerator and a polynomial for its

denominator. For instance,

x

xx

2

2

1

21 x

−

+ 2 x

is a rational expression. Because divi-

sion by 0 is undefi ned, you must exclude values for the variable or variables

that would make the denominator polynomial sum to 0. For convenience,

you can assume such values are excluded as you work through the problems

in this chapter.

Reducing Algebraic Fractions to Lowest Terms

The following principle is fundamental to rational expressions.

Fundamental Principle of Rational Expressions

If P, Q, and R are polynomials, then PR

QR

RP

RQ

P

Q

==, provided neither Q nor

R has a zero value.

The fundamental principle allows you to

reduce algebraic fractions to lowest terms by

dividing the numerator and denominator by

the greatest common factor (GCF).

P

Before applying the fundamental

principle of rational expressions, always

make sure that the numerator and

denominator contain only factored

polynomials.