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

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

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

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

Example Simplify a)b)

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

Example continued b) Solution

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

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

Example Divide and, if possible, simplify: Solution

Example Divide and, if possible, simplify: Solution