I need to show
\[\left(\frac{y}{y-1}\right)^y = \left( 1 + \frac 1{y-1}\right)^y \]
I cannot understand how they made this step! Can someone explain how this works?
I need to show
\[\left(\frac{y}{y-1}\right)^y = \left( 1 + \frac 1{y-1}\right)^y \]
I cannot understand how they made this step! Can someone explain how this works?
We have \[ \frac y{y-1} = \frac{y-1+1}{y-1} = \frac{y-1}{y-1} + \frac 1{y-1} = 1 + \frac 1{y-1}. \]
$ \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...