못하다

First attested in the Yongbi eocheon'ga (龍飛御天歌 / 용비어천가), 1447, as Middle Korean 몯〯ᄒᆞ다〮 (Yale: mwǒt-hòtá). Univerbation of 못 (mot, “cannot; poorly”) +‎ 하다 (hada, “to do”).

• (SK Standard/Seoul) IPA^(key):

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• Phonetic hangul:
  • Though still prescribed in Standard Korean, most speakers in both Koreas no longer distinguish vowel length.

못하다 • (mothada) (infinitive 못해 or 못하여, sequential 못하니)

1. (in the form 지 못하다 (-ji mothada)) cannot (do); to be unable, or impossible (to do)

   집에 가지 못해요. ― Jib-e gaji mothaeyo. ― I cannot go home.

2. (transitive, in the form 를 못하다 (-reul mothada)) not be good at

   Antonym: 잘하다 (jalhada, “to be good at”)

   나는 노래를 못해요. ― Na-neun norae-reul mothaeyo. ― I'm not good at singing.

The second sense is very commonly confused with 못 하다 (mot hada). The contrast is in fact solely orthographic, as there is no prosodic difference between the two and the adverb 못 (mot) can have the sense of "poorly" with all verbs.

오늘은 공부를 못 해요.

Oneur-eun gongbu-reul mot haeyo.

I cannot study today.

공부를 못해요.

Gongbu-reul mothaeyo.

I'm not good at studying.