unit 3 lesson 2: rational expressions. definition of rational numbers a real number r is rational if...
TRANSCRIPT
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.