Rational Function

A rational function is a ratio of polynomials, such as $\frac{x^2-4x+1}{x^3+5x^2-3}$.

If the degree of numerator $\le$ degree denominator, then we can the rational function proper.

• if $<$, then strictly proper

Else, we can it an improper rational function.

Note

Any proper rational function can be expressed as the sum of simpler rational functions, whose denominators are either linear or irreducibly quadratic.