Yep, it's right. You can cancel a -1 to get (2x+2)/(1-x) if you like, but it's the same thing.
Ok so I am doing these exercises and I get to this one:
f(x) = x-2/x+2
so I do y = x-2 / x+2
> yx + 2y = x - 2
> yx - x = -2y - 2
> x(y - 1) = -2y - 2
> x = -2y - 2/y - 1
is the final answer f^-1(x) = -2x - 2/x - 1
??? Sorry I know I did something quirky along the way, any help appreciated