I recently repaired a crack that was worse then yours because there was a vertical gap (part of the concrete path had settled because two years earlier part the soil underneath had been washed out by a plumbing leak).
Since the higher of the two slabs was the correct height I didn't want to do the grinding down that is normally done in this situation.
In order to fill the gap and level the walkway I used a concrete bonding adhesive on the dry and dustfree surfaces to prepare them for applying the new concrete. I used a concrete mixture that seemed to have all the right attributes I was looking for: vertical application, sidewalks, quick setting, non-shrinking. As suggested in the instructions for the concrete bonding adhesive I mixed the concrete by substituting bonding adhesive for the water that was called for in the concrete instructions.
It is the first time I worked with concrete but it seems to have worked just fine. Of course, two weeks is far too early to tell how it will hold up over time.--
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