# Question #27cc4

##### 1 Answer

Let me start from a very simple illustrative example.

Say, we want to decompose

The correct procedure calls for a representation

which results in

and the answer

Without

that cannot be solved for

The idea behind having members of the decomposition with every power of a denominator from 1 to maximum is to be able to accommodate any polynomial in the numerator that can contain a variable

Similar example:

that results in

which can be solved as

Without all three components we would not be able to accommodate any polynomial in the numerator. But, if the numerator does not contain a certain power of

But it's a very peculiar case and, when talking about general rule, it's advisable to retain members with all possible powers of the members of the denominator, from 1 to maximum.