Bad rattle and shake in rear left tire

I have a 2000 Olds Alero GLS that seems to have a large shake at 60 MPH. It also makes a big noise when I go over a bump and seems to rattle when I go around the corner. Do anyone know what the problem might be and whether the repair cost is expensive?
I might also consider fixing it myself if someone could confirm the difficulty of the repair.

First post, looking forward to many more...

Thanks in advance,
Greg

Welcome to the forum....

If you suspect it to be coming from the left rear, the first things I would look at are the rear struts and the rear tires. Check for a broken strut spring and check the strut mounting points to make sure they're tight. Run your hand flat over the tire tread and spin it with the tire off the ground to see if you can feel any unevenness on the tire or see any out-of-round conditions on the tire or the wheel. Also, with the car on the ground, see if the car will push down easier on one side than the other or if it seems to "bounce" freely. This could indicate a blown or broken strut that wouldn't necessarily be visible externally.

Beyond that, look at your bushings where your control arms attach to the body and to the axles to make sure those are tight and the bushings appear to be in good condition.

As for cost and difficulty of repair, it's hard to say until more is known about the source of the problems.

Thanks very much for the response. I had a buddy of mine over and the top of the tire can be moved backward and forward towards the car. It seems to almost pivot back and forth, almost loose. (my back right tire doesn't do that) He seems to think it's a ball joint, but I've never had to deal with something like this in the past. The tire seems round to the touch and rolls evenly and nothing seems broken in the spring or strut area.

Could it be a ball joint?

There is no ball joint on the rear suspension based on the design like the front end. In addition to what was suggested check the torque of the lug nuts. 100 ft-lbs in a star pattern. It sounds like you may have a damaged belt or defective tire so swap it out with the front tire on the same side like doing a tire rotation. Another possibility is bad bearings in the rear hub assembly.

And welcome to AF.