View
217
Download
0
Category
Preview:
Citation preview
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
Recommended