Renting to "Risky" tenant?

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Hi I own a duplex and have been having trouble renting one side of the unit.

What would you do? 

We recently received a tenant lead from an individual with questionable sources of income and limited rental history (discrepancies between the application and credit check). 

My 2nd thought are to rent to her if she can come up with the 1st month rent and the full security deposit. 

At a minimum it'll bring in some income, as opposed to not. 

My rationalization is that I can just evict her if things don't work out. At the moment, it seems like it's no greater risk, than any of my other tenants.