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