1.12 Rational functions

A rational function is an expression

where $f(X)$ and $g(X)$ are real polynomials, with $g(X)$ not the zero polynomial. We use division algorithm to write

We can add, multiply and divide rational functions as if they were fractions.

Definition A rational function is proper if the degree of $f(X)$ is less than the degree of $g(X).$ A rational function is improper if the degree of $f(X)$ is greater than or equal to the degree of $g(X)$.