Simplify (x-(1/x))/(1-(1/x))

I don't get how to do this, can someone please help me? :)

(x-(1/x))/(1-(1/x))

= ( (x^2 - 1)/x) / ( (x-1)/x)
= ( (x-1)(x+1)/x ) * (x/(x-1))
= (x-1)(x+1)/(x-1)
= x+1 , x ≠0,1