What are some causes/solutions for poor drainage?
What is best way to repair slow draining water in bathtub?
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If this just started I would try Draino or Liquid Plumber, if that dosn't work you may need to clean the trap. Seems like I've seen ads for a plastic thing for pushing stuff out of drains or use a piece of wire or a large zip tie and work it into the drain pipe to break up the gunk then try the draino aggain.