3. Rational Expressions A rational expression is any expression that consists of a polynomial divided by a nonzero polynomial. Examples of rational expressions:

5. Example: Consider the function, determine the following. b) The domain of f (x). a) Graph f (x) in the window:

6. c) Find the zeros/roots for f (x). d) Find the vertical asymptotes.

7. Example Simplify: Solution Factoring the numerator and the denominator. Note the common factor of 9x. Rewriting as a product of two rational expressions. Removing the factor 1 9x/9x = 1, clever form of 1

8. Example Simplify a)b)

10. Example Multiply. Then simplify by removing a factor of 1. a) b) Solution a)

11. Example continued b) Solution

12. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Simplify.

13. NO “C” BOMBS!! Look for clever forms of one!! Don’t let the “TERM-ITE” bite you!!

15. Example Divide and, if possible, simplify: Solution

16. Example Divide and, if possible, simplify: Solution