~ㄹ 수 없다 VS ~지 못하다
What is the difference between those two ways of saying that one can't do something? Is there a difference or can they be used indistinctly?

Question

~ㄹ 수 없다  VS   ~지 못하다
What is the difference between those two ways of saying that one can't do something? Is there a difference or can they be used indistinctly?

Answer

~ㄹ 수 없다 has active and temporal nuance.
~지 못하다 has passive and permanent nuance

Both can be used interchangeably in many cases.

Here are the differences.
I cannot swim because I'm tired now.(temporally) 
지금 피곤해서 수영을 할 수 없어요. (more natural)
지금 피곤해서 수영을 하지 못해요.

I cannot swim because I didn't learn swimming.(as usual)
수영을 배우지 않아서 수영을 하지 못해요. (more natural)
수영을 배우지 않아서 수영을 할 수 없어요.

Although I want to eat more, I cannot eat it because I ate my fill. (with the intention)
먹고 싶지만 배가 불러서 이 사과는 먹을 수 없어요. (more natural)
먹고 싶지만 배가 불러서 이 사과는 먹지 못해요.

Answer

"~ㄹ 수 없다" is usually used with verb.
ex) 할 수 없다(하다+ㄹ 수 없다)
       먹을 수 없다(먹다+ㄹ 수 없다)

"~지 못하다" is usually used with adjective.
ex)예쁘지 못하다(예쁘다+지 못하다)
      키가 크지 못하다(크다+지 못하다)
But people don't often use "지 못하다" when they speak.
Instead they use "~지 않다"
ex) 예쁘지 않다(예쁘다+지 않다)
      키가 크지 않다(크다+지 않다)

I hope my answer is helpful :D

Answer

'~ㄹ 수 없다' is usually used when you can't do anything because of the situation.
ex.) 지금 비가 와서 나갈 수 없다.(It's raining now and I can't go out.) - 나가다 + ㄹ 할 수 없다
'~지 못하다' is usually used when you can't do anything because you don't have the ability to do something or you're not capable of doing something.
ex.) 나는 피아노를 연주하지 못한다.(I can't play the piano.) - 연주하다 + 지 못하(ㄴ)다

But... Usually, Korean people use two things without distinction.

I hope my answer is helpful. (:D

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