Fix for sidewalk trip hazard

Watched one DIY show where they dug out under the sidewalk and removed enough of the tree roots to let the side walk settle back into place... they did it from one side and carefully dug it out so as not to break the concrete... but that side walk was over 50 years old and was colored red (original) and they knew they would not be able to match the color if they took it out.

Have a tree company cut the roots from spreading.

I always lay a brick across the cut off root so that if the root grows, it will grow to the side instead of under the concrete again.

If caused by tree roots, which side of walk is it on, yours or the city's? If on city side, make noise until they fix it.

The cheapest and easiest way to repair a problem like you describe is just to patch the areas with concrete.. For example: on low side build it up to high side then taper off over a three to 6 inches. Use a trowel to smooth it out and then cut the line between the two slabs. Once it dries it should be safe and hardly noticeable.

It would be wise to drill some holes in areas your putting in patches so they don't break loose

If it's a temporary fix, use either driveway patch or concrete patch. You can buy pavement patch in a bag or bucket; concrete patch can be found in powder form, to be mixed with water for use.

Does anybody have experience with grinding down the high side? If so, what tools/equipment could be used?