d/dx (x^2 + 1)/x

I need to solve this without quotient rule. Power rule is the most I can use on this problem. The only thing is that I don't see how to get the answer correctly. With quotient rule I can do this but I'm having troubles doing this purely algebraically and with power rule only.

I've tried doing (x^2 + 1)*x^-1, but that gives me 1 as my answer, (which I know is incorrect).

So the answer that Wolfram Alpha is spitting out is 2-((x^2 + 1)/x) , but if I do quotient rule, I get (x^2 - 1)/x^2. So both answers are technically correct, and I think the first one is the one probably possible by algebra.

So can someone push me a step or two in the right direction. I want to solve this so badly. >.< But I have no clue where to start anymore since I've tried several methods to no avail.