chase after
definitions
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to pursue someone or something in order to catch themzh: 追赶某人或某物以抓住他们
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to strive to achieve or obtain somethingzh: 努力争取或获得某物
examples
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The dog chased after the ball.
狗追着球跑。
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She chases after her dreams every day.
她每天都在追求她的梦想。