Step two is wrong. Distribution doesn't work across multiplication, only addition. [spoiler]a(b+c)=ab+ac but a(b*c)=abc[/spoiler]I have no idea wtf textbook you're using that has that in there.
EDIT: I realised that this likely isn't from a textbook, but my point stands. Wherever you saw that "how it's supposed to be done" is wrong, both with the distribution, and where they said that "x^(n-(n+1))=x^1". That doesn't even make any damn sense.
I will attempt to solve it in my 3AM haze. Prepare for a stupid mistake.
NOTE: I'm going to assume that x does not equal zero, because then solving this req's more writing that I don't want to do.
(x^n / x^n+1) / [x^2 * (x * x^-3)]
(x^n / x^n+1) / [x^2 * (x^-2)]
(x^n / x^n+1) / [x^0]
(x^n / x^n+1) / [1]
(x^-1) / [1] = x^-1