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못한 게 is a colloquial form of "못한 것이"
못한 것이 is composed as
못하(다) + (으)ㄴ + 것+이
못하다 means "not be able to do something" or "inferior to"
(으)ㄴ is a particle used for translating a verb into an adjective at past tense.
것 means "thing, matter"
이 is a subject particle
못한 것 means "something which someone could not do" or "something which someone was inferior to somebody"
present tense : 못하는 것
future tense : 못할 것
ex)
내가 너에게 말 못한게 있어
There's something I didn't tell you.
좀더 오래 있으면서 프랑스어를 배우지 못한 게 아쉽네요.
Too bad you didn't stay a bit longer and learn to speak French.