When I try to open Facebook on my iPad it flashes open then closes right away how do I fix this problem?

Sounds like a crash. Have you tried removing and reinstalling FB app?

delete the app (hold down on the icon until you see an x and hit x) and redownload - if that doesn't work, make sure all your applications are closed - swipe up on the preview screen in multitasking screen - http://support.apple.com/kb/HT4211 - or reset network settings > settings> general > reset - just make sure you know your wifi password because you will have to enter it again.