Hello,teachers: I got confused."I love you both "and "I love both of you".Are they same?Is "I love both you."correct?If "both of " and "both" can replace each other in any situation?Thanks for your time and reply.Katie
Both are correct, and they carry the same meaning. I suppose that will hold in almost any situation, but I cannot guarantee it, this being English.
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Thanks very much for your time and help.Did you mean all of the 3 sentences are correct?
Sorry, I didn't pay close attention to the 3rd one.

"I love you both "and "I love both of you".-- Fine.
"I love both you." -- Frequently heard in spoken English. 'Of' is probably ellipted.
Thanks again.I get it.
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first two are correct. in the first "both works as a determiner to pronoun YOU", in the second it works as a pronoun which can stand by itself in the sentence, but in your case you specify those two people by writing "both OF YOU".

"I love both you" is grammatically incorrect, because if you use "both" with pronouns (We/us, you, they/them) it MUST stand AFTER the pronoun you modify.
I like them both.
They hate us both.
We both dislike the idea of going to McDonald's.

However, if you use verbs TO BE (ARE, WERE), you should put BOTH after them, you can't separate subject from verbs ARE, WERE. For instance.

We are both hated by them. (Not We both are hated by them)
These girls are both hot! (not These girls both are hot.)
They were both there. (not They both were there)