In a sentence like this:
He read a book and he discussed it with his friends.
Is it correct to leave the second "he"? (He read a book and discussed it with his friends.) I suppose it is, because I've encountered multiple examples.
However, I am not sure if it is still correct for the following sentence:
He read a book but he didn't understand it.
Is it correct to leave the second "he" in this case? (He read a book but didn't understand it.) Is there a rule explaining this?
EDIT: I would like to add another example that doesn't sound natural at all:
You've never been to New York, but (you) know what you'll find there.
Different tenses, positive and negative parts. Is it still possible to leave out the subject in the second part?