We are just being introduced the the derivative concept and I was wondering if I understand this correctly.

We got the formula f(x) lim h->0 (f(x+h) - f(x)) / h

One example says: Find derivative for the function f(x)=x/(x-1)

Does this like correct:

1. (x/x-1+h) - (x/(x-1) / h

The x/x-1 - x/x-1 cancel out

Leaving you with H/H

so the derivative is 1??