1. Factor Each Expression 1. 2. 3. 4.

2. Section 8.4

3. Multiplying and Dividing Rational Expressions Remember that a rational number can be expressed as a quotient of two integers. A rational expression can be expressed as a quotient of two polynomials.

5. Remember, denominators can not = 0. Now,lets go through the steps to simplify a rational expression.

6. Step 1: Factor the numerator and the denominator completely looking for common factors. Next

7. What is the common factor? Step 2: Divide the numerator and denominator by the common factor.

8. 1 1 Step 3: Multiply to get your answer.

9. Looking at the answer from the previous example, what value of x would make the denominator 0? x= -1 The expression is undefined when the values make the denominator equal to 0

11. How do I find the values that make an expression undefined? Completely factor the original denominator.

12. The expression is undefined when: a= 0, 2, and -2 and b= 0. Factor the denominator

13. Lets go through another example. Factor out the GCF Next

14. 1 1

19. Now try to do some on your own.

20. DAY 2

22. Remember how to multiply fractions: First you multiply the numerators then multiply the denominators.

23. The same method can be used to multiply rational expressions. 11111 1111

24. Let’s do another one. Step #1: Factor the numerator and the denominator. Next

25. Step #2: Divide the numerator and denominator by the common factors. 1 1 1 1 1 1

27. Remember how to divide fractions?

28. Multiply by the reciprocal of the divisor. 1 1 5 4

29. Dividing rational expressions uses the same procedure. Ex: Simplify

30. 1 1 1 1

31. Now you try to simplify the expression:

33. Now try these on your own.

34. Here are the answers: