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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?

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That you have it in such a form is perhaps the best tool. Graph the expression in J, a and q to see where it potentially blows up, and then see if that relation occurs and is nicely representable in terms of your four favorite variables. My guess is that a close to 0 requires attention as does a close to (q/J + J). Gerhard "Ask Me About Blowing Up" Paseman, 2012.12.11 –  Gerhard Paseman Dec 11 '12 at 23:44

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