In general, if a denominator of degree n factorises completely, it will separate into the sum of n terms, each of which is of the form
In general if there is a power of a linear factor in the denominator there will be denominators consisting of ascending powers of that factors the denominators of which are all pure numbers.
If the degree of the numerator is less than the degree of the denominator and the fraction separates into partial fraction, there will be:
One term for every irreducible factor. The degree of the numerator of this term will be one less than the degree of the denominator.
One term for ever repeated root in the denominator,. If the repeated root is of then the terms in the run will take the forms
where all theare numbers,