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    $\begingroup$ If expr is not polynomial in x, either Collect[ expr, x, f] or Collect[expr, x] often simply returns expr. I don't have a reference for this, but I realized it while looking into this question (see comments). $\endgroup$ Commented Sep 22, 2017 at 22:23
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    $\begingroup$ Perhaps you might be able to separate your input into pieces that are polynomial in (x+_)^_, and then do Collect[polnomialPart, (x+_)^_, whatever] on those. But note e.g. the behavior of Collect[a Sqrt[x + y] + b Sqrt[x + y] + d (x + y)^(-1/2), (x+_)^_], which has head Times. $\endgroup$ Commented Sep 22, 2017 at 22:29
  • $\begingroup$ Finally, you might want to do Together on your expression and do Collect on the Numerator only. $\endgroup$ Commented Sep 22, 2017 at 22:29
  • $\begingroup$ @jjc385 Thank you for the pattern suggestion (x+_)^_ with caution. I'll play around with it. I will check on the possible inherent limitation of Collectnot working for non-polynomials, and maybe I'll modify the post accordingly (remove the Simplify issue). As for Together, please see my added clarification in the paragraph starting with the words "my ultimate goal". Anyway your comments are appreciated! $\endgroup$ Commented Sep 22, 2017 at 23:25