After 20 years in our house, the patio has settled about 3 inches below the house / carpport slab.. It is not a problem except where the patio exits into the carport walkway.. where I am worried about someone falling or tripping.. I thought of slab-jack BUT very expensive and since I doubt there is rebar in the patio, they would not rule out cracking the patio slab.. I just want to make a ramp like transition from the carport to the patio.. BUT how and with what.. I am sure a small amount of concrete would crack and pall apart.. Any ideas?? If the transition went out 18" to 24" would be ok..

Maybe the photo shows better what I am describing..