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what is the difference between ㄹ 수가 있다 and ㄹ 수 있다

I've seen 'ㄹ 수가 있다 ' loads of times before but can't quite get if it's different to 'ㄹ 수 있다', just as an example:
문제를 풀 수가 없어요
문제를 풀 수 없어요
Any help is greatly appreciated! :D

For learning: Korean
Base language: English
Category: Language

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    Here '가' is used to emphasize "문제를 풀 수 없어요".
    "문제를 풀 수가 없어요" has a sense of "I tried to solve the problem many times, but I couldn't, so you are a bit frustrated."


    \^o^/

    I think they are almost same. "문제를 풀 수가 없어요"sounds a bit emphatic. "문제를 풀 수 없어요" jsut gives the fact that "I can't solve the problem". "문제를 풀 수가 없어요"also gives the fact that "I can't solve the problem and I got some stress about that so I'm frustrated"

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