is "you've nothing to offer me." correct?
I've alway thought it should be "You have nothing to offer me.",but I did hear "You've nothing to offer me." from TV 《Camelot》.So???

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Yes, it's alright.

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I think that the words that you wrote are correct.

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It is all the same!
"You've " is just a contraction of 'You have' as JacquiD mentioned. That means a shorter form used informally.
However it is not true, because I have  got something to offer you; I can try to answer your questions ;)

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'You've' is the contracted form of 'you have'. Although American English speakers only normally use the contraction of 'have' when it's the auxiliary verb, (I've got to go now), British English speakers use the contraction when 'have' is the auxuliary and the main verb. So the sentence is correct.

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基本上have不做助动词的时候是不能用`ve的形式来发音的