～得る・~得ない ～うる・～えない ...can

「できる・～の可能性がある」
can

Vうる means "that can be done, that is possible" Vえない means something that cannot be done or which is impossible. Note that this form is not used to indicate something that is impossible because of lack of ability. Also note two dictionary forms - positive form us うる・得る while negative form is えない・得ない

Vます, drop ます and add 得る

（１）これは仕事を成功させるために考え得る最上の方法です。
This is the best method I can think of to make this job succeed.

（２）この事故はまったく予測し得ぬことであった。
This accidend was something that could not have been foreseen.

（３）これは彼でなくてはなし得ない大事業である。
This is a great business that could not have been without him.

（４）この事故はいつでも起こり得ることとして十分注意が必要だ。
As this accident is something that could happen at any time, you need to take a great deal of care.

（５）彼が事件の現場にいたなんて、そんなことはあり得ない。
That he was at the site of this incident is something that just couldnt be.

（６）考え得るかぎりの手は尽くしたが、問題の解決には至らなかった。
I exhausted all the ways I could think about, but didnt reach a solution to the problem.

（７）捜し得るかぎり捜したが、その書類はとうとう見つからなかった。
I searched as much as I could search but could not find those documents.

（８）でき得るならば、独立して事業を始めたい。
If I am able to do it, I would like to be independent and start a business.

（９）こんなに低い山で遭難することはあり得ないと思う。
I think you can't meet danger on a mountain as low as this.