$\left(\frac{y}{y-1}\right)^y = \left( 1 + \frac 1{y-1}\right)^y$ Can someone please help me with this? I cannot understand how they made this step! Banging my head over this for far too long now :(

Thank you Lukas

-

We have $\frac y{y-1} = \frac{y-1+1}{y-1} = \frac{y-1}{y-1} + \frac 1{y-1} = 1 + \frac 1{y-1}.$

-
Thank you very much Martini! Perfect! –  Lukas Arvidsson Oct 19 '12 at 15:32

$$\frac{y}{y-1} = \frac{y-1+1}{y-1} = \frac{y-1}{y-1} + \frac{1}{y-1} = 1+ \frac{1}{y-1}$$

There's the line of thought I use. You add and subtract one (adds up to zero, so it's allowed), then you rearrange everything to get the final result.

Edit: crud, not quick enough...

-
Thank you very much, i had totally forgotten about that "method". But now it is clear! –  Lukas Arvidsson Oct 19 '12 at 15:33
This is the same @martini did (+1). :) –  Babak S. Oct 19 '12 at 16:30