Let me introduce you to my friend or let me introduce my friend to you . Are both correct and if so, do the have the same meaning? Thanks for your help.

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They’re both correct.

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Both are correct, but using the Passive Voice here complicates the sentence unnecessarily. I would use the Active voice (subject + verb + object), it sounds more natural.

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Both are correct. The difference is whom you are emphasizing. 
Introduce my friend to you…you are emphasizing your friend

Introduce you to my friend…emphasizing “you”

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