In the negative-potential form, 切(き)れない will attach to the 連用形(れんようけい) form of other verbs, to express that a particular action is ‘unable to be completed’. Let’s look at some examples.
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大盛(おおもり)頼(たの)むの?いくらあなたでもここの大盛(おおもり)は食(た)べきれないと思(おも)うよ。
Are you going to order the large one? I don't think you can possibly finish the portion they serve here.
あの山(やま)は一日(いちにち)では登(のぼ)り切(き)れない。
You can't possibly finish climbing this mountain in one day.
Unlike
切(き)る, which usually attaches to verbs to show that something was done to the point of running out,
切(き)れない often implies the exact opposite. This means that the (A) verb cannot be completed specifically because there is too much/many of something in order to finish it.
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宇宙(うちゅう)には数(かぞ)え切(き)れないほどの星(ほし)がある。
There are too many stars in space to count.
この肉(にく)は厚(あつ)すぎて歯(は)では噛(か)み切(き)れない。
This meat is so thick that it is not possible to chew with your teeth.
切(き)れない may also imply that something cannot be done ‘to the point of satisfaction’. In this case, the feeling of dissatisfaction is what the speaker considers too much to overcome.
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私(わたし)のこの気持(きも)ちは言葉(ことば)では表(あらわ)しきれない。
I cannot possibly explain this feeling of mine with words. (Cannot explain satisfactorily)
楽(たの)しみ過(す)ぎて待(ま)ちきれない。
I am so excited that I can't wait. (Cannot wait satisfactorily)