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On the IRS publication 527, Residential Rental Property, section 5 Personal Use of Dwelling, contain a lot of information about pro-rating based on days rented versus not rented. On the worksheet 5-1 Percentage of expenses allowed for rental. This seems to imply you get to allocate your utilities annually based on this percentage. This would be a lot simpler than actually trying to allocate utility costs for renters time.

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