Partial fraction decomposition,how? I need to decompose this fraction:
$${x^2+1\over (x-1)^3\cdot(x+3)}$$
I tried to write it up like this:  $${A\over (x-1)}+{B\over (x-1)^2}+{C\over (x-1)^3}+{D\over (x+3)}$$ 
But now i get $$A\cdot(x-1)^5\cdot (x+3) +B\cdot (x-1)^4\cdot (x+3) +C\cdot(x-1)^3\cdot (x+3) +D\cdot (x-1)^6 =x^2+1$$  which is not correct i think.
What should i do?

I think your expression should be:
$$
A\cdot(x-1)^2\cdot (x+3) +B\cdot (x-1)^1\cdot (x+3) +C\cdot (x+3) +D\cdot (x-1)^3 =x^2+1
$$
because the LCM of $(x-1)$, $(x-1)^2$, $(x-1)^3$ and $(x+3)$ is $(x+3)(x-1)^3$
