Algebra 2

5-4 Rational Algebraic Expressions

5-4 Rational Algebraic Expressions

WARMUP Simplify:

2 4

5

1

2

2 3 8

6 5 4

3

7

8

4

x yz

xy z

x yz

xy z

5-4 Rational Algebraic Expressions

Recall that a rational number is one that can be expressed as a quotient of integers.

A rational algebraic expression, or rational expression, is one that can be expressed as a quotient of polynomials. Examples:

2 22 1

2 2

4 3 4, , ( 4)

7 1 4

xy x x xx x

y x x

5-4 Rational Algebraic Expressions

A rational expression is in simplified form, or in simplest form, when it is expressed as a quotient of polynomials whose greatest common factor is 1.

In other words, look for common factors

5-4 Rational Algebraic Expressions

Simplify:

2

2

2 ( 2)

4 ( 2)( 2)

( 2)

( 2)( 2)

2

x x x x

x x x

x x

x x

x

x

5-4 Rational Algebraic Expressions

Try this:

2 3

2

3 5 2

6 5 1

x x x

x x

5-4 Rational Algebraic Expressions

A function that is defined by a simplified rational expression in one variable is called a rational function.

2( )

xf x

x

5-4 Rational Algebraic Expressions

Find the domain and the zeros of function :

2

3 2

2 7 3( )

2

x xf x

x x x

5-4 Rational Algebraic Expressions

Examples:

5-4 Rational Algebraic Expressions

Homework:

p. 228 # 1 – 27 ODD

5-4 Rational Algebraic Expressions

5-4 Rational Algebraic Expressions

5-4 Rational Algebraic Expressions

5-4 Rational Algebraic Expressions