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PowerExpand, Apart, Simplify


In dealing with complicated expressions involving rational polynomials I find
PowerExpand, Apart and Simplify to provide the best simplifications. However,
it is not clear to me in which order to apply them for the best result. They
certainly don't commute! Any clues would be much appreciated.

On the same note, I have not been able to find any way to make Mathematica
tell me that the following expression equals 1 (using the built-in functions,
that is):

Sqrt[3 x^(4j)+x^(12j)]/(x^(2j)Sqrt[3 + x^(8j)])
(x,j real and positive)

Any ideas?

Thanks,
Dani




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