If you see gear oil leaking out around the pinion flange on your differential, it is likely that the seal inside is the cause of the leak. You should first check that the breather for the axle housing is not plugged, as this can lead to increased pressure inside the axle when it heats up and that can cause oil leaks as well. A related issue is if the nut on the pinion flange has worked loose and you can feel a little play at the flange. This may cause a slight leak and you'll also feel a slight vibration in that driveshaft at speed when you just back off the gas pedal. In this condition, you have unloaded the shaft and any play in the flange can lead to a vibration that will not be there under load.
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