We have always been told to pay off your balances in total, but that can be a good thing initially it can hurt in the long term. Having an active account is an account you are currently paying on, and a inactive account is one you have stopped paying on whether or not you still owe the debt this includes charge offs and collections. So when you pay off your balance in full it becomes inactive since you are no longer making any payments on that debt, and there is nothing for the creditor to update to the credit bureau.
This will improve your credit score at first, but creditors and the credit bureau like to see active accounts and if your accounts stay inactive for a period of 6 months or longer that account has now become dormant and will start to have a negative effect on your credit score.
This is why for the long term its not good to have an account that is inactive you want to have at least a small balance on your accounts to keep it from becoming dormant it does not really matter how small, your creditors just want to see some type of on time payments being made to that account, and just keep on paying your balances off every month. Especially if its an account you had for over 3 years, creditors like to see a long credit history, and it does you no good to close accounts you had for a long time and keep accounts that are fairly new.
An active account in good standing will do more to build your credit and keep it healthy than an account that is inactive and paid off. So the moral of the story never close revolving long history accounts unless you plan on establishing new credit, because it will lower your credit score. If you do choose to close an revolving account, close the ones that are under 2 yrs, since creditors like to see accounts over 3 yrs old.