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