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    $\begingroup$ Without a complete, even if simpler, example to work with, perhaps this is will work: Replace[expr, term_ /; MemberQ[Numerator[term], (x | y)^i_ /; i > 4] -> 0, 1]?? It assumes the expression for your rational function has been expanded in the way you describe. Please clarify whether this is right or wrong. $\endgroup$ Commented Jul 11, 2014 at 1:06
  • $\begingroup$ PolynomialReduce is a good function for this type of thing. $\endgroup$ Commented Jul 11, 2014 at 14:12