Treat this as two separate properties. On the rental side, you pay capital gains tax on the entire gain, including depreciation recapture. On the part that used to be a personal residence, you can exclude 250k/500k, but pay depreciation recapture from depreciation since it was converted to a rental.
Simplified example. You purchased the entire structure for 200k, and sell it for 600k, no capital improvements. Assuming a 50/50 split, you would have a gain of 200k plus depreciation recapture on the rental portion, and a 200k gain plus smaller depreciation recapture on the personal side. Applying the exclusion on this property eliminates the capital gain, but not depreciation recapture. You can't apply any if the "leftover" exclusion to the rental side.
