This has been annoying me for a long time. I want a rational function to be represented in the form
But this seems to be quite difficult. Mathematica really loves to factor things out. //ExpandAll usually gives me a sum of bunch of rational functions. I just want the numerator to be a straightforward polynomial and the denominator to be a straightforward polynomial.
I can //Together to get a single fraction and //Expand the numerator and denominator separately, and then combine them by hand, but that is very annoying and it feels like there should be a command to do this. The form I wrote above is the most common rational function form, so why would it be so difficult to arrive at?
For example what do I need to do the fraction below to get it to be a polynomial divided by a polynomial?
-2/n^3 + (32 n)/(1 - 8 n^2 + 16 n^4)