Transform rational equations to polynomial equations

Question

I have a list of rational equations and I would like to convert it to a list of polynomial equations. I know that none of the variables and none of the denominators could ever be 0. 
So far I have tried:

removeDenom[ a_ == b_ ] := Numerator[a]Denominator[b] == Numerator[b]Denominator[a];

ratToPol[eqn_] := removeDenom @* Together @ eqn;

Which seems to do the trick for rational equations with small exponents of the variables but for larger ones, e.g.

x[1]^24566482 x[2]^25894864 x[3]^36056313 x[5]^2 x[6]^2==(x[1]^10050244 x[2]^10878704 x[3]^15147675 x[6]^8)/x[5]^4+x[1]^39374641 x[2]^41453905 x[3]^57720898 x[5]^4 x[6]^2 x[7]^2

I get the error General::lrgexp Exponent is out of bounds for function 1.

Any ideas on how to proceed? It would be nice if there was a way without using Simplify or other higher-level functions for which it is unknown how they operate exactly.

LouisB · Answer

This function works for the example expression

removeDenom[a_ == b_] := Block[{
   u = Times @@ Denominator /@ a,
   v = Times @@ Denominator /@ b},
  Expand[u a v] == Expand[u b v]
  ]

It multiplies the LHS by all the denominators it finds on the RHS and vice versa.

The polynomialGCD error occurs in Together, so don't use ratToPol.  Just use removeDenom[p]

Also, removeDenom does NOT play nice with subscripted variables u and v, but it seems to work with x.

Transform rational equations to polynomial equations

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