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I have a cement floor in my bathroom witch I am planning on installing tile, what is the best way to bridge that gap for tile installation?
For cracks less than 1/4" wide use concrete caulk, then tape/mesh over the crack.
LATICRETE® Blue 92 Anti-Fracture Membrane
If the crack is due to movement over a wood substrate, then you'll need to beef up the joists and or plywood to handle tile. If over a slab a crack isolating membrane will help, but you still have to honor the joint all the way through the tile assembly, which means locating a 'soft joint' over the crack OR a somewhat complicated 3 tile wide, very specific installation method.
If you have vertical displacement (one side of the crack is higher than the other) then there are other issues.
For all things tile, head on over to the John Bridge Tile Forum where you can start your own thread, post pictures and get answers specific to your home.