〜がたい
hard to (accept, believe, forgive)
Verb ます-stem + がたい
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がたい means something is very hard or almost impossible to do, for emotional or moral reasons: 彼がうそをついたとは信じがたい, "it's hard to believe that he lied".
It attaches to the ます-stem of verbs of thinking and feeling: 信じる, 理解する, 受け入れる, 許す, 忘れる. It's a formal, written word.
Compare にくい (N4), which is used for practical difficulty: 読みにくい字, "handwriting that's hard to read". がたい is about the mind resisting: 受け入れがたい提案, "a proposal that's hard to accept".
It works like an い-adjective: 忘れがたい思い出, "an unforgettable memory". 得難い ("rare, precious") and ありがたい ("grateful") come from the same word.
Examples
彼がうそをついたとは信じがたい。
It's hard to believe that he lied.
その提案は受け入れがたい。
That proposal is hard to accept.
彼の行動は理解しがたい。
His behaviour is hard to understand.
忘れがたい思い出になった。
It became an unforgettable memory.
これは許しがたい行為だ。
This is an unforgivable act.