What is the inverse of f(x) = x/x-1 ?

this is my attempt to solve it:

y = x / x-1

y(x-1) = x

hence x(x-1) is the inverse.....

however, substituting with x=5 gives......

5/4=1.25

so pluging this is the inverse function should give 5, right?

lets see:

1.25(1.25-1) = 1.25*.25= 0.3125. WRONG!!

can anyone tell me where I went wrong?

thanks