General aviation pilot reported a near miss while descending into the path of another aircraft trailing behind the reporters aircraft; while receiving VFR flight following with ATC. The pilot maneuvered away from the other aircraft upon becoming aware of the other aircraft.

Narrative

I was flying noticed I was getting really close to BJC [airport] at 9500. I was on VFR Flight Following but ATC started talking a lot and I decided that I would descend. I visually checked the area; but didn't see the plane behind me. I forgot to check ADS-B; that was mistake #1.I then proceeded to descend in the practice area on DEN Approach frequency without even referring to the practice area frequency; mistake #2. I then got a traffic warning on my ADS-B in the plane and on my iPad and looked behind me to see a plane doing steep turns; I immediately tried to climb the plane back up to 9200'. I think ATC noticed because they stuttered and kind of sighed in resignation when I saw the plane very close to me; he asked if I saw the traffic and I confirmed; but at this point I was climbing away from the traffic headed back to BJC. I stayed on a little longer; descended to 6500 and did the visual approach with no further issues.This was definitely a near miss. I will make sure to check all available resources; not just look in front of me visually; I've definitely learned from this failure and will have this incident burned into my brain.