Unit 3 Lesson 2: Rational

Expressions

Definition of Rational Numbers

• A real number r is rational if and only if there exist integers a and b ,such that

• You can tell that a number is rational because its decimal is either

_________________________ or ________________________.• The rational numbers are closed under the four main operations

(addition, subtraction, multiplication, and quotient division), which means that the sum, difference, product, and quotient of rational numbers are always ________________________.

( 0)b arb

repeating terminating

rational

Definition of a Rational Expression

A rational expression has the form

Where f(x) and g(x) are polynomials ()

Rewriting in Lowest Terms

Example 1: 5 3

2 3 2

x x

x x

State any restrictions on the variable.

Rewriting in Lowest Terms

Example 2: 11

11

11

x

x

State any restrictions on the variable.

Arithmetic Operations

Example 3: 3

2

5

32914

xyxy

State any restrictions on the variable.

Arithmetic Operations

Example 4: 2

2 2

6 8 7

5 14 16

a a a

a a a

State any restrictions on the variable.

Arithmetic Operations

Example 5: 2

4 1

1 2 3

x

x x x

State any restrictions on the variable.