We've all seen the definition, but for some reason I still don't understand the logic behind it. This is the part of the definition that I have a problem with:

f (x+h) - f (x) / (x+h) - x

I understand that (x+h) - x = h.

If this is the case, will this be true f (x+h) - f (x) = h ...?

Thus, h / h ?