Question 893776
Use x,y.
{{{y=(2x-3)/(x-1)}}}
Now interchange {{{x}}} and {{{y}}} and solve for {{{y}}}. 
This new {{{y}}} is the inverse. 
{{{x=(2y-3)/(y-1)}}}
{{{x(y-1)=2y-3}}}
{{{xy-x=2y-3}}}
{{{2y-xy=3-x}}}
{{{y(2-x)=3-x}}}
{{{y=(3-x)/(2-x)}}}
{{{f^(-1)(x)=(3-x)/(2-x)}}}