What's the difference between ~得ない【えない】, as in, say, 届き【とどき】得ない【えない】, and ~eない, as in 届けない【とどけない】? As far as I can tell they both mean "it can't be done," "it's impossible", but is there a difference in connotation or a subtle difference?

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    Don't forget that for ichidan verbs, your -eない would be ~(ら)れない
    – Angelos
    Aug 22 '16 at 21:16
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    Does japanese.stackexchange.com/questions/1865/… or japanese.stackexchange.com/questions/2682/… help to answer your question? (Basically, using 得る is more academic in style)
    – virmaior
    Aug 23 '16 at 0:02
  • @virmaior Yes, particularly the second, but to be honest I'm too new to Japanese to make too much sense of the answers - while I think the information is present there I'm going to need it separated and summarized to properly understand it. Aug 23 '16 at 7:31
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    I don't know why, but we say 届く/届ない, rather than 届ける/届ない, to mean "can/can't reach"... We usually use 届ける/届けない to mean "deliver/don't deliver", as a transitive verb, not potential.
    – Chocolate
    Aug 24 '16 at 6:52

届けない doesn't mean "something can't reach" but "to not deliver something" as chocolate says.

Since 届くis an intransitive verb that doesn't stand for one's volitional action, 届く doesn't have the potential form.

As for difference between ~得ない and potential forms, the former stands for possibility under a certain condition while the latter does one's ability or capability. So you can't use potential forms when the subject of a sentence is linguistically inanimate like plants or something that doesn't move by itself, in other words, you can say この木は大きくなり得ない or …大きくならない for "this tree can grow big" but not この木は大きくなれない (in average people's sense).

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