5.1.2

 A rational function is one that can be expressed as a ratio of two polynomials.  Some examples: y =, f(x) =, g(x) =, h(x) =  Here are some examples that are NOT rational functions: y =, y = Why are they not rational functions?

Example: Some of the trickier algebra problems require you to simplify expressions like:. What do we do? Eliminate the x −1 term: Recall that x −1 simply means …, so we can eliminate the x in the numerator by multiplying both the top and bottom of the original fraction by x. Since x · x −1 = 1, we now have. Eliminate the y −2 term: Now we multiply the top and bottom of the fraction by y 2 to get the answer. Since the numerator and denominator have no common factors, we are done.