Struktur
Verb[stem]+ える(1)
Exceptions:
Verb[stem]+ えない(*)
Verb[stem]+ えた(*)
Verb[stem]+ えなかった(*)
(1) うる
(*) For negative, past and negative past forms, only conjugations of える are used
Rincian
Standard
Tentang 得る・得る
得る 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)'.
Compared to できる, which means that the potential to do something exists, 得る 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 教える becoming 教えうる, rather than 教ええる.
Fun Fact
得る 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 あり得る 'possible', and あり得ない 'impossible'.
Terkait
Contoh
--:--
それはあり得る。
That can be possible!
その対策は考え得る。
It is possible to consider that countermeasure.
災害はいつだって起こり得る。
Disaster can occur at anytime. (there is a possibility that it can occur)
対応次第でストライキは回避し得る。
A strike can be avoided depending on how it is dealt with.
耕し得る土地を持っている方は田植えができます。
People who own arable land can plant rice. (can be farmed)
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得る・得る – Diskusi Tata Bahasa
Balasan Terbaru (total 4)

DarkConfidant
if a verb stem ends with え is it more likely to be うる or am I reading too much into the examples?

gyroninja
I think you are reading too much into it (though maybe don’t fully trust me since I’m making an informed guess). うる is the classical Japanese reading of 得る so it will be more rare to show up and likely has some set phrases where it appears.

simias
It may have changed since you commented this but now the entry for 得る does mention:
Despite this, there is a tendency for うる to be the preferred spoken choice when the kana that appears before it is え
Punya pertanyaan tentang 得る・得る? Yuk, bergabung dan ikutan berdiskusi, bertanya, serta belajar bareng!
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