For , this gives . Replacing, transposing, collecting like terms, and dividing by , we get
.
Hence and ; and ; or and , and finally, or . So that we obtain as the partial fractions:
.
It is useful to check the results obtained. The simplest way is to replace by a single value, say , both in the given expression and in the partial fractions obtained.
Whenever the denominator contains but a power of a single factor, a very quick method is as follows: