Grammar Info
N2 Lesson 1: 1/21

is able to, can, possible

Verb[ます+ える(1)

Verb[ます+ ない(*)
Verb[ます+ (*)
Verb[ます+ なかった(*)

(1) うる
(*) For negative
past and negative past forms
only conjugations of える are used
Verb[ます+ えます(1)

Verb[ます+ ません(1)
Verb[ます+ ました(1)
Verb[ます+ ませんでした(1)

(1) For polite forms
only conjugations of える are used
Register Standard
使用域 一般
得(え)る is a る-Verb that has the meaning of 'to gain', or 'to acquire'. When attached to the conjunctive form of verbs, it takes on the nuance of 'for (A) to be possible', or 'to be able to (A)'.
  • もし出来(でき)得(え)るならば、2年後(ねんご)に会社(かいしゃ)を立(た)ち上(あ)げたいと思(おも)っている。
    If it's possible, I'm thinking of starting a company in two years.
  • いくら気(き)をつけていても、交通(こうつう)事故(じこ)は起(お)こり得(え)るものだ。
    No matter how careful you are, it's possible for a car accident to occur.
Compared to できる, meaning that the potential to do something exists. 得(え)る means something closer to 'there is a possibility that (A) can be done', or 'the possibility to do (A) has been gained'.
Caution - 得(え)る may be seen as either える or うる. The primary difference between the two being that うる is a relatively old form that is often seen in literature, and spoken far less frequently than える. Despite this, there is a tendency for うる to be the preferred spoken choice when the kana that appears before it is え, such as 教(おし)える becoming 教(おし)えうる, rather than 教(おし)ええる.
  • そういう事(こと)はセクハラにもなりえるので、そういう事(こと)はやらない方(ほう)がいい。
    Things like that can be considered as sexual harassment, so you shouldn't do that.
  • 考(かんが)えうる事(こと)は、すべてこの企画書(けいかくしょ)に書(か)いておきました!
    I wrote everything I can think of on this proposal!
Fun-fact - 得(え)る is far more formal/bookish than できる. However, there are several set phrases that are very common in daily speech that use this particular grammar point, such as あり得(え)る 'possible', and あり得(え)ない 'impossible'.
  • うん、それもあり得(え)るね...
    Yeah, that is also a possibility...
  • 電気代(でんきだい)がまた値上(ねあ)がりするみたいだよ。マジあり得(え)ない
    It looks like the electricity bill is going to go up again. There's no way.
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Firefighters are people you can trust.
It is possible to consider that countermeasure.
People who own arable land can plant rice. (can be farmed)
Tae Kim's Japanese Grammar Guide
Page 127