Solving rational function equations by converting to polynomial equations

[zengmao]

symbolic_solve fails for some equations involving rational functions, unless the user manually multiplies out denominators to convert the equations into polynomial equations. Example below. Can the conversion be automated?

julia> using Symbolics, Nemo

julia> @variables x;

julia> symbolic_solve(x ~ 1/x, x) # denominators cannot be handled
┌ Warning: This expression cannot be solved with the methods available to ia_solve. Try a numerical method instead.
└ @ Symbolics ~/.julia/packages/Symbolics/e7UFe/src/solver/ia_main.jl:176

julia> symbolic_solve(x^2 ~ 1, x) # multiply both sides by `x` to get polynomials
2-element Vector{BigInt}:
 -1
  1

(Julia 1.10.5, Symbolics 6.4.0, Nemo 0.45.7, SymbolicUtils 3.5.0)

[ufechner7]

Duplicate of #1268