Selley's have a relatively new product called "GrowCrete".
It comes in 2kg bags, you mix the powder with water and spread on the concrete slab.
The chemicals in the paste react with the existing concrete and makes it swell up to 15% and it also makes it malleable so you could shape the old slab into more of a ramp to lessen the gap.
Or not. Get in touch with your feminine side....and embrace "The Shit". It exists for a reason.