Question 889576
ASSUMING you really mean {{{(x+1)/(x-1)}}}:
-
{{{x=(y+1)/(y-1)}}}
{{{x(y-1)=y+1}}}
{{{xy-x=y+1}}}
{{{xy-x-y=1}}}
{{{xy-y-x=1}}}
{{{y(x-1)-x=1}}}
{{{y(x-1)=x+1}}}
{{{highlight(y=(x+1)/(x-1))}}}


Maybe a graph of each would help to be sure.


Original f(x)
{{{graph(300,300,-10,10,-10,10,(x+1)/(x-1),x)}}}



The worked inverse - which as algebraic expression is the same - would not be different.  Observe the symmetry around the line y=x shown in green.