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The typical rational function has the form p(x)/q(x) where p and q are polynomials. p(x) is called the numerator and q(x) is called the denominator. Example: In the rational function. which simplifies to simplifies to (x+2)/(x-3), but the x = 2 is NOT in the domain of g(x) whereas it IS in the domain of (x+2)/(x-3).
To understand the behavior of a rational function it is very useful to see its polynomials in factored form. The polynomials in the numerator and the denominator of the above function would factor like this: The Domain. Now the roots of the denominator are obviously x = -3 and x = 6.