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It is super easy, don't worry.
Jack it up, of course..
You have to unbolt the differential cover, and drain the oil from it (use a 13 m.m.). There will still be some, so use a drain pan.. The cover will be siliconed on there, so it will not be easy to break it loose. Just be careful not to bend it.
Once the cover is off, get a magnet. There is a bar that you will have to remove out of the middle of the gear assembly. Usually, also 13m.m. wrench, or an allen bolt. Rotate the axle until you can access the 'bolt'. Remove it. Push the bad axle in, to access the c-clip inside the differential. This is where the magnet may come in, sometimes it (c-clip) just falls out...
Once the clip is removed, the axle can be slid out. Replacing the bearing is straightforward. You have to use a new seal, of course. Keep in mind, that the axle may be damaged, replace it if it is not in the same condition as it was new (the bearing surfaces, and check for bent)
Installation is reverse of removal. Be sure to change the brake linings, they are no good.
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The cover can be put back on with black RTV silicone, and refill it with atleast GL-5 gear lube.