If I rent out my primary home and pay rent elsewhere, can the rent I paid be used to offset my rental income?

[sunshineInTheRain]

Let me put into numbers, for example, I collect $4000 rent each month, and the property tax, mortgage interest adds up to $2000 per month. I will not consider the depreciation part in this case, as the depreciation you deducted always comes back when you sell it.  And I pay $2500 rent to rent an apartment. Is there a way to take use the $2500 as rental expense? It is theoretically right that in order to rent out my home to get $4k rental income, I have to pay $2500 cost to find myself a place to live. 

[xmasbaby0]

There is not a rent deduction or credit on your Federal return.  If your state has anything for renters you will be prompted to enter your rent info when you complete your state return.  As far as I know, the states that have anything for rent are Arizona, California, Connecticut, Hawaii, Indiana, Iowa, Maine, Maryland, Massachusetts, Michigan, Minnesota, Missouri, New Jersey, Rhode Island, Vermont, and Wisconsin.