Question: manipulating numerator and denominator

Something simple enough, I want show (g^n) / (g^n -1) = 1 / 1 - g^(-n) step by step in maple. 

The problem I'm having is getting maple to freeze the terms.  Maple likes to simplify before I can have it do what I want.  I suppose I could make everything a name and show it manually but I would like to force maple to do it. 

first setting


so first multiply the numerator and denominator by g^(-n)

have maple show the operation explicitly  g^n*(g^(-n)) / (g^n-1)*(g^(-n))

then multiply it out and show 1 / (1-g^(-n))

and finally one more step I would like to add, have maple output 1 / (1-1/(g^n))

Please Wait...