If you bought a duplex for 300,000 and had costs that could be added to the basis of $2,000, then the adjusted basis would be $302,000 for the property.
Assuming equal sq ft, $151,000 would be the basis of the rental property and $151,000 would be the basis of the personal home.
If you had $1,000 in deductible expenses, $500 could be deducted on Schedule E against rental income and $500 could be deducted on Schedule A as an itemized deduction. These expenses would be deducted in the year that the expenses were incurred.
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