Would it be unwise to seek fiction and non-fiction agents at the same time?

Please forgive me if this is a question you've seen a hundred times; I couldn't figure out how to search for previous similar posts without calling up nearly every post in AW.

I just started seeking an agent for a proposed non-fiction book and want to keep writing so that I don't get rusty or feel the rejections so acutely. Being around AW has gotten me interested in polishing up and seeking an agent for a finished novel mouldering away on my hard drive.

If I get it ready before managing to sell the non-fiction idea, would it be nuts to try to find separate agents for each project at the same time? Should I try instead to find agents who handle both? If I manage to get an agent to represent one or the other, would she tell me to drop the other project to focus on whichever one she agreed to represent?

I know it's wildly unlikely that I would manage to sell both at the same time, and even a stretch to sell one. I just wondered how to handle two genres or if I'm crazy for considering doing both at once in the first place. Thanks in advance for any help and sorry for being so ignorant on this one!

Good idea--thank you!