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JLPT N2Written, formalA verdict

がたいhard to (believe, forgive, forget)

"Hard to", because your mind or conscience won't go along: hard to believe, impossible to forgive. It is written and formal, and goes with a small set of verbs, mostly of thinking and feeling.

How to form it

Verb ます-stem + がたい (a small set of verbs)

信しんじます → 信しんじがたい, 理り解かいします → 理り解かいしがたい. It changes like an い-adjective and goes straight before a noun: 忘わすれがたい一いち日にち.

The common ones
信しんじがたい (hard to believe), 理り解かいしがたい (beyond understanding), 許ゆるしがたい (unforgivable), 忘わすれがたい (unforgettable), 耐たえがたい (unbearable), 近ちか寄よりがたい (unapproachable). These are words in their own right. On most other verbs がたい isn't said.
Tone
A weighty verdict, often indignant or deeply moved.
Where you'll meet it
Essays, editorials, reviews, speeches. In conversation people mostly say 信しんじられない, 許ゆるせない, 忘わすれられない.

In use

Not for physical difficulty

This key is rusty and hard to turn.

The key is the trouble, so it is にくい. Nobody says 回まわしがたい.

It is hard to believe that everything in this record is true.

Nothing is in the way but your own mind: がたい.

とは言いいがたい

とは言いいがたい, "can hardly be called", is a measured way to say that something isn't so.

Close neighbours

にくい・づらいN4

The everyday "hard to", on any verb: it takes effort, or it feels awkward.

かねるN2

"Cannot": the polite, formal refusal of service language, or a mind that can't settle on something.

Check yourself

1Which one fits?

この靴くつは小ちいさくて、(  )。

Choose an answer to see why.

2What is the writer saying?

この計けい画かくは成せい功こうしたとは言いいがたい。

Choose an answer to see why.

More detail

Two that people do say in conversation, when choosing or judging:

More sentences