We may have to express expressions such as
in the form
Notice first that 
factorises into
We can write,
Ignore the first term here and multiply throughout by
We get
after cancellation.
The procedure now is to eliminate the A term by putting x=2
Eliminate the B term by putting x=-4
Then
If we have a denominator which includes an
term which does not factorise, we have to include a term,
term in the answer. In general we have one term for every term in the denominator which does not factorise, and for that term, the highest power of
in the numerator is one less than the highest power ofin the numerator.
Example:
Multiply out by
and cancel to give
(1)
Put
into (1) to make the first term on the right hand side zero. We get,
If we put
we eliminate
Now put
