Question: simplify - getting the "simplest" form....

Recently i'm noticing that mathematica is basically a mind-reader with their FullSimplify function, whereas maple even with simple expressions does not show what I would consider optimal (I agree this will be somewhat subjective).

Here is a trivial example:
ex1:=(2*sqrt(N__s) + N__s + 1)/(2*N__s + 2);

none of these are any help
simplify(ex1, size);
simplify(ex1, symbolic);
simplify(ex1, sqrt);
simplify(ex1, sqrt, symbolic);

The ideal expression I would like to see here is:
1/2 + sqrt(N__s)/(N__s + 1)

Am I doing it all wrong (suppose I don't know of this simple form beforehand)?

Mathematica gets it right - see the following screenshot:

I'm finding this a lot... especially when hyperbolic functions and sqrt's are involved ("symbolic" option helps sometimes, but often the expressions are still not what I would consider "simplifed").

Please Wait...