老师好，
Laboratory rats and mice live up to 40 percent longer than usual when fed a diet thathas at least 30 percent fewer caloriesthanthey would normally eatbut that otherwise contains all necessary vitamins and nutrients.
请问老师，第二个划线处为何不是that they would normally eat？是由于跟第一句划线共用a diet that中的that吗？还是说本来就无需加that？为何可以省略呢？
when the downtown shopping district has rebounded before, the business premises of a failed business were typically taken over by a business of the same kind ashad been there before.
请问老师，划线处为何不是that had been there before呢？为何需要省略呢？
答疑网这种问题和解答不少的。你可以查阅。
简单回答如下：
假如把as和than剖析为连词，不作从句成分，则比较分句势必是一个结构不完整的分句，需要留出一个空位。该空位就是主句比较项在从句的对应项。即主句比较项的对应项需要在从句中省略，不可出现。
你的句子简化如下：
The diethas at least 30 percent fewer caloriesthanthey would normally eat .
划线部分分别为主句的比较项和其在从句中的对应项（空位）。
The business premises of a failed business were typically taken over by a business of the same kind as had been there before.
划线部分分别为主句的比较项和其在从句的对应项（空位）。
假如把as/than剖析为比较替代词，则as/than需要在从句作成分。如此剖析的结果就是从句需要是结构完整的分句。
The diethas at least 30 percent fewer caloriesthanthey would normally eat.
than在从句中作eat的宾语。从句不缺成分，不可再加that。
The business premises of a failed business were typically taken over by a business of the same kind as had been there before.
as在从句中作了主语。从句不缺成分，结构已经完整。
无论以上哪种分句，都不可以再给从句加成分。二种剖析的结果是一样的，可谓殊途同归。