一、规范的表达:
The reason why he wants to sell his house is that he needs a lot of money for his operation. 
The reason that he wants to sell his house is that he needs a lot of money for his operation.
The reason he wants to sell his house is that he needs a lot of money for his operation.
二、不太规范的表达,但不能说错:
The reason why he wants to sell his house is because he needs a lot of money for his operation. 
The reason that he wants to sell his house is because he needs a lot of money for his operation.
The reason he wants to sell his house is because he needs a lot of money for his operation.
 
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    There are several reasons why the treatment didn't work. 治疗不见效有几个原因。(摘自《朗文多功能英汉双解词典》第五版)
The reason why I came here was to be with my family. 我到这里来的原因是要跟我的家人在一起。(摘自《牛津英语用法指南》第三版)
Do you know the reason that they're closing the factory ? 你知道他们要关闭这家工厂的原因吗?(摘自《牛津英语用法指南》第三版)
The reason she doesn't like me is that I make her nervous. 她不喜欢我的原因是我让她紧张。(摘自《牛津英语用法指南》第三版)
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