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How to simplify x^a/x into x^(a-1) OR how to solve...?

asked 2013-07-17 04:05:49 -0500

Qiang gravatar image

Can any body show me which function simplifies x^a/x into x^(a-1)? A related question is how to solve x^a == 2*x to have x = 2^(1/(a-1))? Mathematica works out these questions well, but I'm a huge fan of Sage/Maxima, and eager to get an answer using Sage. Thanks!

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answered 2013-07-17 05:28:20 -0500

tmonteil gravatar image

updated 2013-07-17 05:34:53 -0500

Concerning your first question, you can try this:

sage: x, a = var('x a') 
sage: expr = x^a/x      
sage: expr.full_simplify()
x^(a - 1)
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Thanks! This works. But how Sage or Maxima solve the above equation still troubles me a lot.

Qiang gravatar imageQiang ( 2013-07-17 22:53:12 -0500 )edit

Yes, i agree that sage: sage: x, a = var('x a') sage: solve(x^a == 2*x, x) [x == 1/2*x^a] is not very satisfactory.

tmonteil gravatar imagetmonteil ( 2013-07-20 12:12:37 -0500 )edit

While full_simplify works on x^a/x, it already fails as soon as x is replaced by something slightly more complicated, like (1-x).

Gustav Delius gravatar imageGustav Delius ( 2013-08-23 02:35:59 -0500 )edit

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Asked: 2013-07-17 04:05:49 -0500

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Last updated: Jul 17 '13