1. 7.1: Simplifying Rational Expressions March 31, 2009

2. Topics for review Multiplying monomials Graphing Factoring

3. Multiplying monomials

4. Graphing

6. factoring Find ac and b Find two numbers that add to equal b and multiply to equal ac Split b in half, using these numbers Factor by grouping

7. Factoring 5x 2 -8x-4=0

8. Factoring 9x 2 +4x-5=0

10. This week Monday: review Tuesday: lecture (7.1) Wednesday: work day Thursday: lecture (7.2) Friday: quiz (7.1 only)/work day

11. Objectives Simplify rational expressions Identify rational functions Simplify rational functions Graph rational functions

12. Standards Addressed Algebraic Relationships –Analyze the nature of change of each variable in a non-linear relationship as suggested by a table of values, a graph or a formula –Evaluate and make a table for two-variable formulas and match a graph or table of values to its formula Calculations and Estimations –Apply the associative, commutative, and distributive properties to simplify computations with real numbers

13. What does rational mean? Rational comes from the word ratio, which means fraction! Rational expressions are expressions that can be written as fractions.

14. Precluding division by zero Any value divided by zero is undefined. Find the value for x for which the following rational expressions are undefined.

15. A few more

16. Evaluating a rational expression To evaluate means to solve for a given value of x. Evaluate the following rational expression for x = 3.

17. A few more Evaluate for x= -2.

18. Simplifying a rational expression Monomial: one term Simplifying monomials: Cancel out common factors

19. A couple more

20. Simplying non-monomial rational expressions 1)Factor the numerator and the denominator, using the GCF or the ac method (sometimes factoring out -1 can be helpful) 2)Cancel out common factors

21. An example Try this one:

22. Try another

23. And another…

24. Identifying a rational function A rational function must be able to be written as a ratio, even if the denominator is simply 1. There cannot be any square roots.

25. Simplifying a rational function 1)Examine the denominator. Determine what value of x will make the denominator equal zero. Write x ≠ (that number). 2)Then simplify as before. 3)The answer will be the simplify version, plus part 1.

26. Try it Try this one.

27. Try another

28. Graphing a rational function 1)Simplify the function. 2)Note what x cannot equal (≠). 3)Plug that value in and determine the y value. Mark an open circle at the ordered pair (x, y) that you have just found. This is called a hole. 4)Graph normally.

29. Try it Remember this one?

30. Try another What about this one?

31. Your assignment Pages 489-490 2-36 even 40-66 even