1. (x + 2)(x2 – 2x + 4) Warm-up: Factor: x3 + 8
HW: pages (2-10 Even, 20, 24, 28, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76)

2. Rational (Fractional) Expressions

3. Objective: Find the domain of an algebraic expression
Simplify a rational expression
Multiply and divide rational expressions
Chapter 14 Outline

4. Rational Expressions
Quotients of polynomials are called rational expressions.
For example

5. Finding the Domain
Domain the set of real numbers for which an algebraic expression is defined. Domain Restrictions the set of real numbers for which the algebraic expression is undefined.

6. Domain D: All real numbers or D: (- , )
Ex1) Find the domain of 2x3 + 3x + 4
D: All real numbers or
D: (- , )

7. Domain D: All real numbers except x = 5 Or D: {x| x ≠ 5}
Example 2: Find the domain of the rational expression.
Denominator cannot be zero!
Restriction: 4x – 20 = 0
4x = 20
x = 5
D: All real numbers except x = 5
Or D: {x| x ≠ 5}
Or D: (- , 5)  (5, )

8. Domain
Example 3: Find the domain of the algebraic expression.
The square root of a negative number is not a real number!
Or D: [2, )

9. Simplifying Rational Expressions
Simplifying a rational expression means writing it in lowest terms or simplest form.
Fundamental Principle of Rational Expressions
If P, Q, and R are polynomials, and Q and R are not 0,

10. Simplifying Rational Expressions
Simplifying a Rational Expression
1) Completely factor the numerator and denominator.
2) Apply the Fundamental Principle of Rational Expressions to eliminate common factors in the numerator and denominator.
3) You must list any domain restrictions removed from the original rational expression in order to maintain equality for all values of the domain.
Warning!
Only common FACTORS can be eliminated from the numerator and denominator. Make sure any expression you eliminate is a factor.

11. Simplifying Rational Expressions
Example
Simplify the following expression.

12. Simplifying Rational Expressions
Example
Simplify the following expression.

13. Rules of Multiplication and Division
If P, Q, R, and S are polynomials, then
Multiplication
Division

14. Example
Perform the indicated operation and simplify

15. Example
Perform the indicated operation and simplify

16. Rules of Addition and Subtraction
If P, Q, R, and S are polynomials, then
Addition
Subtraction

17. Example
Perform the indicated operation and simplify

18. Examples Method 2
Simplify

19. Examples
Simplify

20. Summary: Find the domain of an algebraic expression
Simplify a rational expression
Multiply and divide rational expressions
Chapter 14 Outline

21. Sneedlegrit:
Simplify. What are the domain restrictions for the rational expression?
HW: pages (2-10 Even, 20, 24, 28, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76)