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.