Hi, here's a proposed manual entry for solve_rat_ineq. As far as I can see it's currently not documented at all except for the comments in the source code. (The .texi file is based on those comments.) My thanks go to Volker van Nek for the actual code!
Oops, in the "Limitations" paragraph the word "removable" should be, well, removed. "Regular" discontinuities may also lead to spurious solutions:
(%i1) load(solve_rat_ineq)$
(%i2) solve_rat_ineq(1/x^2>=0);
(%o2) all
Thank you Gilles for your generosity in sharing the files. I'll review them and then I'll tell you.