Selecting the proper rational fraction
Suppose
where
in which the denominators are factors of
From these factors we can determine the form of the partial fraction decomposition using the following two rules: Linear Factor Rule:For each factor of the form
where A 1, A 2,..., Am are constants to be determined. Quadratic Factor Rule:For each factor of the form
where A 1, A 2,..., Am, B 1, B 2, …, Bm are constants to be determined.
|
is a rational function; that is, 
and 
are polynomial functions. If the degree of 
where 
is a proper rational fraction; that is, the degree of 
is less than the degree of 
are rational functions of the form
or 
and 
.
, the partial fraction decomposition contains the following sum of m partial fractions:
