Question 833070
Do you  mean, {{{(x+1)/(2x+1)}}} ?
What kind of inverse?  Additive?  Multiplicative?  Something else?  


According to the category you assigned with your question, either you want {{{-(x+1)/(2x+1)}}}  or you want {{{(2x+1)/(x+1)}}}.



Imagining that you want the inverse function for {{{y=(x+1)/(2x+1)}}};
you can try switching the purposes of x and y, their positions in the equation, and solve for y.


{{{x=(y+1)/(2y+1)}}}
{{{x(2y+1)=y+1}}}
{{{2xy+x=y+1}}}
{{{2xy-y=-x+1}}}
{{{(2x-1)y=-x+1}}}
{{{y=(-x+1)/(2x-1)}}}-------the inverse


That is not the correct way to handle the notation for finding function inverse, but the method IS very practical.  Better use of notation is to give a function name to your original function, such as f(x), and then call the inverse as f^-1(x).  You also use these notations in the algebraic steps performed.