Simplification not working as hoped.

I have an expression that ultimately becomes:

f:(exp(x)+exp(x/2))/(exp(x/2)+1);

I've tried various simplification routines:


                              ratsimp(f);
                              trigsimp(f);
                               radcan(f);


The only one that works is radcan().   Is there a flag that
would make the other ones work?  Alternately, is there a function that
forces the exponentials to be represented as sums of hyperbolic
functions?