I have a somewhat complicated symbolic expression of the form $\frac{J-a+\frac{q}{a}}{J(J-a)+q}$, where $J,a$ and $q$ are themselves affine functions of four other variables $d,r,c,s$, and I want to find some tame upper bound for the expression in terms of $d,r,c,s$. Sometimes this works well by simplifying the original expression with the use of a symbolic math package (I use MATLAB) and staring at the result for long enough, but this time it didn't.

So, I wonder: is there some automatic tool that helps with this kind of problem? Maybe something similar to AutoGraphiX?