Question

前半部分是定语从句还是同位语从句？The reason why he was dismissed is that hewas careless.

The reason (why he was dismissed )is that hewas careless.

Answer 1

应该是定语从句
你已经在why he was dismissed 处打括号了，省略不看，这个句子的意思仍然通顺。原因是他太粗心了。
reason这个先行词一定要用why来引导，语法书有的，你可以去查一查，加入why he was dismissed这个后置定语，意思是他被解雇的原因是因为他太粗心了。

Answer 2

这句话中既有定语从句又有宾语从句
The reason is that hewas careless里的that是引导宾语从句的
The reason why he was dismissed 这是定语从句，也可以说是原因状语从句。
why he was dismissed 并不是reason的内容，而是 he was careless，why he was dismissed 是对reason的限制。故而是定语从句。

Answer 3

定语从句
先行词reason 去掉括号里的从句句子结构依然完整
原因（为什么他被解雇的）是他太粗心了。

Answer 4

定语从句

Answer 5

同位语。。。。。