We just had a new addition put on our slab, ranch-style house. It is about a 10'x40' addition in the center of our home. The problem is the slabs do not match. The old slab is about 1 inch higher in most spots. This room also has the front door in it, which doesn't give us much room to build up the floor. We also have cork tile flooring on the old slab that we can remove - it's only about a 1/4" high. What's the best way to make the floor level, since the contractor thinks he didn't do anything wrong?