My friend is going through a divorce, but I really don't want to give him a place to stay, despite the fact that I know it would help him ut.
Why don't you want to help him?
I'm too busy with my own life.
It is fair to keep your priorities straight if you have a busy life. I would ask yourself why you do not want to host and find other ways to support him so that you do not ruin the friendship.
I'm going to let him fend for himself as far as a place to live goes, but I'm also going to see how he does it and how he's doing.
You should be supportive of your friend, but it's okay to set boundaries in the process. Having him live with you might not be ideal, but you should still be there for him in his time of need.