Mike, a simple and effective way to do this is ude a piece of Scluter metal at the edge.you will see a 1/8" wide piece at the edge when it is installed. it protects the tile edge and your feet from sharp edges.Pull the carpet back and pad.Feather out the area with a cement based patching compound for about 30-36" out.after this dries replace your carpet tack strip on top of this feathered out area and restretch the carpet to the tile edge and trim with a sharp carpet knife.Thats it perfect transition.
For cutting off your door,Run Tape over bottom edge, mark where you want to cut it and score it several times with a good sharp utility knife.Set up a fence for your Circular saw and clamp it tight so the blade stays on the outside edge of the score mark.Be sure your blade is very sharp( a new carbide is reccomended here).
Now carefully cut the bottom,peel the tape and reset your door.
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TIP YOUR TILE MAN, His Retirement plan is not nearly as lucrative as yours and his waning years will be far more painful to boot.
He gives much so you can have a Beautiful Home!!
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