Well, I don't know if you can use that, but I use some sort of inspection to get the values of A and B.

Take the fraction:

Now, what value do you have to assign to x so that one denominator becomes 0?

We put x = 3.

So, you find this:

And put x = 3, to get 1/36. This is the value of A.

From this, take x = -3 now:

Evaluate and you get -1/36, which is the value of B.

Now, you are left with:

There are only two constants to find now