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The problem is most likely in one of the bearings in the rear end. There are bearings on the pinion (part that connects to the driveshaft) and there are bearings on the carrier (inside the housing, holds the ring gear). To properly repair this problem, it is best to completely disassemble the rear end and inspect all of these bearings, replacing those that are bad. It takes special tools to properly service these bearings and to set up the gear mesh when reassembling the rear axle. Therefore it is best done by a professional.