1. Simplifying

2. 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.

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

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

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

6. 1 1 Step 3: Multiply to get your answer.

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

8. How do I find the values that make an expression undefined? Completely factor the original denominator. And see which values for x make the denominator 0.

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

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

11. 1 1

12. a = 0, 3

13. Now try to do some on your own. Also find the values that make each expression undefined?

14. Here are the answers:

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

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

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

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

19. Step #3: Multiply the numerator and the denominator. Remember how to divide fractions?

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

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

22. 1 1 1 1 Next