No wonder they're driving you crazy. Both sentences are perfectly correct. They are, however, informal.
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Actually... I wonder whether the problem isn't with the use of the auxiliary verb in the second clause. We don't need it. If were to break the sentence into two separate sentences, we would say 'He doesn't work (very) hard' and 'She works hard.' In the case of the first sentence, we need the auxiliary verb do/does, but in the second sentence, not only do we not need it, but it is grammatically