Painting over wallpaper?

Anyone have personal experience with painting over wallpaper?? We are considering doing it in our dining room. We borrowed a steamer off of a friend and even with doing that and scoring up the wall the wallpaper isn't coming off easily and it's leaving wallpaper pieces on our wood trim. That and the plaster under the wallpaper is in pretty rough condition. I've been researching the ways to paint over it so we're going to primer, drywall patch then paint. I just want to see if many people have had success with this before we go ahead and do it. Thanks a lot