hang by a thread
(1) thread “线”
(2) hang by a thread字面意思“被一根线吊着”，表示“岌岌可危，千钧一发，命悬一线”
英语解释为be in a very dangerous situation and may not continue。
(3) 可用于形容感情、关系、生活等出现了问题，情况危急，或生命遇到危险等。
例
Andy: My personal life is hanging by a thread. That's all.
我的个人生活岌岌可危。
Nigel: Join the club. That's what happens when you start doing well at work, darling.
彼此彼此，亲爱的，这说明你的工作开始步入正轨了。
We're all just hanging by a thread.
咱俩现在都岌岌可危了。《摩登家庭》
濒临破裂
on the rocks
(1) on the rocks字面意思“触礁”，表示“（关系）濒临破裂，出现危机”
英语解释a relationship that is on the rocks is having a lot of problems and is likey to fail soon。
(2) 常用于形容婚姻，出现问题，濒临破裂；也可用于企业，表示濒临破产。
例
Is her marriage on the rocks?
她的婚姻触礁了吗？
I think their marriage is on the rocks.
我觉得他们的婚姻出现危机了。
处于崩溃的边缘
on the brink of collapse
(1) brink基本义是“悬崖峭壁的边缘”，引申义为“（事情快要发生的）边缘”，一般指坏事
(2) on the brink of sth. “处于......边缘，濒临......”
(3) on the brink of collapse “濒临倒闭，濒临破产，处于崩溃的边缘”，主语可以是公司、谈判、婚姻等
例
The couple's marriage is on the brink of collapse.
这对夫妇的婚姻处于崩溃的边缘。
The company is on the brink of collapse.
这家公司濒临破产。
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