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Is there any math formula reduction tools?

for example convert:

$\frac{a(a+1)}{2a}$

to:

$\frac{a+1}{2}$

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    Actually, it should be $(a+1)/2$, not $a+1/2$, since $a+1/2$ means $a+(1/2)$.2011-10-08
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    Actually that's only true if you assume that $a\neq0$.2011-10-08
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    Another way of putting Michael's comment: parentheses are cheap. Use them when there is a potential source of ambiguity.2011-10-08

2 Answers 2

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Mathematica has the command FullSimplify, for example. One can use it for free on WolframAlpha; here it is in action simplifying $\frac{a(a+1)}{2a}$ into $\frac{a+1}{2}$.

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    Is there any desktop software or plugin?2011-10-08
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    matlab can do this, by using sym method.2011-10-08
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    There are both mobile apps and widgets: http://products.wolframalpha.com/2011-10-12
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Two more ideas (free software for the desktop):

  1. Maxima: a widespread free symbolic-math software; can even be configured to simplify wrt special trigonometric expressions (I use this if I have complicated expressions, derivatives and/or integrals)
  2. (examples like yours above can even be handled by Pari/GP; but is not specialized on symbolic expressions and can simplify polynomial/series expressions, and -but only to a very small extent- rational functions. Likely not what you want)
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    +1 for Maxima, let's add link: http://maxima.sourceforge.net/2011-10-12