切れない|きれない

1. 1Cannot finish or do all of something because there is too much of it.Ex. 1
2. 2Cannot fully hold back or endure something, often a feeling (e.g. 待ちきれない, 耐えきれない).

A neutral expression used in both speech and writing, often with a stated reason such as 多すぎて or 量が多くて. It is the negative of the potential form of きる, so it says the action cannot be carried through to completion, not that it cannot be started. It differs from にくい and がたい, which describe difficulty, and from ようがない, which means there is no way to do it. Fixed expressions such as 数えきれない (countless) and 待ちきれない (can't wait) are very common.

• きるN3「きる」is the affirmative form, meaning to do an action completely or for a state to reach its extreme (e.g. 「疲れきる」). 「切れない」is the negative of its potential form 「きれる」, meaning unable to finish or fully accomplish, so the two cannot be swapped.
• がたいN3「がたい」also attaches to the ます-stem, but means something is mentally or objectively difficult, almost impossible (e.g. 「信じがたい」), with no sense of 'unable to finish'. Its tone is formal and literary, and it generally cannot be interchanged with 「きれない」.
• にくいN4「にくい」means an action is hard to do or unlikely to happen, while 「きれない」means the action is possible but cannot be completed due to quantity or degree. Both attach to the ます-stem and cannot be swapped: 「食べにくい」means awkward to eat, while 「食べきれない」means unable to eat it all.
• ようがない / ようもないN2「ようがない」means there is no means or way, so the action cannot even be started, whereas 「きれない」means the action is possible but cannot be fully completed due to quantity or degree. Both attach to the ます-stem and cannot be swapped, as in 「食べようがない」vs. 「食べきれない」.

きる is the affirmative form (do completely, e.g. 食べきる), while きれない says completion is impossible. がたい (formal; psychologically hard to do, e.g. 信じがたい) and にくい (the action is hard or tends not to happen, e.g. 読みにくい) describe difficulty rather than an inability to finish, and ようがない means there is no way or method to do it at all.