Question about frequencies (vocals and piano)

In studying some on frequencies, and doing some mixing, I understand that one of the battles is “carving out” some of the piano to allow the vocals to shine through.

My question: would having the pianist play the low part (left hand) an octive lower and the high part (right hand) an octive higher be wise to help with that battle? Or is it best to keep the piano in the same octive as the vocals?

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