First, set-up:
You can see that if you cover-up
, then
But that is not going to give us b and c, so let's do it in the saver way.
Put the RHS over a common denomintor:
We have
[Stop for a moment. Let
: Then we have
. So
. The cover-up method was really this in disguise. You can see why it doesn't work for finding b and c -- there is no value of x which can make
equal to zero. So if in general you have a partial fraction form of
, then you cannot find A and B by covering-up -- in other words, the denominator have to be linear for the cover-up to work.]
We have:
(expanding the right-hand side).
(writing it in terms of descending powers of x).
(factoring out the x's out).
Now, compare the coefficients:
We have
.
.
, and since
, we get
, hence
.
Therefore
It should of course take a much smaller space to write-up, but that's Mr Beefcake's attempt at being clear.