I have ripped out old ceramic tile from a half bath in my 100 year old house so that I can lay a new ceramic tile floor. Under the ceramic tile was a subfloor which I believe is made of cement board, but it is damaged in some places and also has the old adhesive stuck to it. Should I remove this, and if so, any suggestions on how to do so? Or can I simply lay another layer of cement board over this older one? Also, I can see the original hardwood underneath of this subfloor. Is it a bad idea to lay ceramic over hardwood floors? There is basement underneath. Thanks for helping out an unexperienced tiler...

hardwood under tile