Simply add any other elements to these two rules that require container clearing, and everything should show up on the screen
One thing troubles me though. If you left div contains actual content (writing or images), that content should not be obscured. Using a clearing mechanism such as what I've posted is meant to force the containing element to open up vertically to accommodate elements floated within. It sounds to me like something in the left div simply isn't showing up on the screen, or is only being partially displayed. Out of curiosity, is the purpose of the left div solely to display a background image? If so, your description would now make perfect sense (and the clearing mechanism would not necessary be the right answer).
The best thing to do would be to post a link to the issue you're having. It'll be very difficult to give a proper diagnosis without seeing the problem firsthand