Answer
$y=\frac{1}{x-1}+1\quad \mathrm{or}\quad y=\frac{x}{x-1}$
$\:$
$ $
Work Step by Step
$y=\frac{1}{x}$
Moving the graph up by $\ 1\ $ unit will change the $\ y\ \rightarrow\ y-1$. And moving it to the right by $\ 1 \ $ unit will change the $\ x\ \rightarrow\ x-1.$
So the equation of the shifted graph would be:
$y-1=\frac{1}{x-1}$
$y=\frac{1}{x-1}+1$
$\mathrm{or},$
$y=\frac{x}{x-1}$
