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

Questions
1

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
Algebraic Calculations—Wolfram Documentation 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

2

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

3

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

4

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.

5

1806re01.png
1806re01.png576×687 28.6 KB

6

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.

Capture.PNG
Capture.PNG703×134 3.65 KB

Best
Chris

7

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.