Concrete slope from garage to driveway

I have a garage that opens onto a shared driveway. The garage floor is level but the driveway slopes down along the garage opening. There's a small ramp of concrete that connects the floor of the garage to the driveway pavement. This slope of concrete is falling apart and is at such a sharp angle that my car bottoms out when coming out of the garage.

I'm not too familiar working with concrete, but this seems like a small enough job that I could probably tackle it. I would need to remove the old concrete and pour a new slope. The garage opening is about 20 feet. Seems simple enough, but am I fooling myself here?

Also, if I were to do it, what kind of joint/spacer material am I likely to need to join the new slope to the garage and pavement? (both concrete, although the pavement is pretty coarse, with some stones in it)

Thanks in advance,
Mat

 

If you are down in Florida Some code call for that step that the door goes downinto . That is so rain cant blow back under the door into the garage.
But you could take out what you have and put all new back in there . Home depot and Lowes have a cement patch mix in a bag that will work for you.

ED