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to beat; to attack (an enemy); to do away with; to finish off
彼は強敵を一人で見事に遣っ付けた。
He magnificently defeated the strong enemy alone.
悪役を主人公が遣っ付ける場面が好きだ。
I like scenes where the hero defeats the villain.
問題を素早く遣っ付けてしまおう。
Let's quickly take care of the problem.