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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).
In this case, one speaks of a rational function and a rational fraction over K. The values of the variables may be taken in any field L containing K. Then the domain of the function is the set of the values of the variables for which the denominator is not zero and the codomain is L.he adjective irrational is not generally used for functions. The rational function is equal to 1 for all x except 0, where there is a removable singularity. The sum, product, or quotient (excepting division by the zero polynomial) of two rational functions is itself a rational function.