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Rearrange equation with mathematica s.t. variable only in denominator?

Posted 9 years ago

Hej all,

I am struggling with an equation which I would like to rearrange so that the variable is in the denominator only. I tried combinations of many possible ways to put expression in different forms https://reference.wolfram.com/language/tutorial/PuttingExpressionsIntoDifferentForms.html but nothing worked out so far.

Is there any possibility to tell mathematica to do it? (file attached)

Thanks in advance. I would be very happy if you have an idea how to solve this

Best, Chris

Attachments:
POSTED BY: Chris Roof
6 Replies

How about

d = Denominator[f[x]];
Map[Inactive[Divide][#/x^Exponent[#, x], d/x^Exponent[#, x]] &, 
 Collect[d*f[x], x]]

It uses Inactive of Mathematica 10 to avoid re-arrangements of numerators and denominators.

POSTED BY: Gianluca Gorni
Posted 9 years ago

Hi all,

thanks for your help. I did not manage to solve the problem in the way I wanted and did it manually. Additionally I solved it with mathematica as shown in the picture.enter image description here

Best Chris

POSTED BY: Chris Roof

enter image description here

POSTED BY: Simon Cadrin
Posted 9 years ago

Consider that the function has a zero, and that any "rearrangement" that expresses the same function must also exhibit this zero. If, in the new expression, x does not appear in the numerator, then the only way for the function to provide the zero, at least as a limit, is for the denominator to go to infinity. But the only way to do that with finite values for x is for a term of the denominator to itself be rational and to contain x in its denominator.

But this is not really different from the clearly unwanted solution where num/denom is rewritten as 1/(num^-1 denom), which is trivial and I think misses the point.

POSTED BY: David Keith
Posted 9 years ago

Hi Okkes,

thanks for looking at it and the manipulations. As you said - there is still the variable in the numerator ... For the spacing: I adjusted the previous file in order to be clearer.

Any further ideas or how can I check if it is even possible (or if I am wasting my time ...)

Best Chris

POSTED BY: Chris Roof
Posted 9 years ago

you forgot to put space between some variable.. I tried it didnot work.

Attachments:
POSTED BY: Okkes Dulgerci
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