I need a pen to write with.with一类的介词有时在句末,有时又没有,这是什么语法?

当不定式动词是不及物动词时,应加相应介词.
The room is too small for us to live in.
The ice is too thin to skate on.
the chair is very comfortable to sit on.
I have a firend to wait for.
这些不定式都是不及物动词,所以后面的介词不能省略.
The book is difficult to understand.
understand是及物动词,所以后面不跟介词.