well, you must practice, then you will be fine,
Yes, i myself cannot stress that enough here. The first rainbow road course i did, i was falling quite frequently for a while. But: i took the time to practice the course over and over, long enough for me to get good at it. After enough time, i was able to play the course very flawlessly and i was able to do it without frequent falls.
This was on super mario kart for the super nes, by the way. I remember times i would race my older sister to see if i could beat her. She was extremely skilled, by the way. She knew how to get the perfect start almost every time (i didn't for this version of mario kart, but i nailed it for later versions of mario kart), plus she literally never fell off the edges on any course, and what would happen at times (if i was lucky enough to get a brief lead over her, of course) is she would have a red shell and hold it until i passed her, and then she would get me with it and get way ahead again.
My falls werent frequent either (except for a lot of the special cup stages, not counting rainbow road here), but she still beat me nearly every time. I actually kind of laugh remembering all of this. I actually had a lot of fun with her, even though i didn't beat her very much.
Keep in mind though; my sister had a lot of prior experience and practice with the game than i did. She didnt magically get that good; she had a lot of practice. What im getting at here is that anything is possible to conquer if you put enough time, practice, and effort into whatever it may be that you are trying to accomplish. Be patient: nothing comes magically. You need to keep trying until you have it mastered, or are able to play better.
Dont give up; i know its hard and can be very frustrating trying to finish anything of high or extreme difficulty. I got pretty frustrated with my own share of things as well, gaming or something else. But i didnt let my frustration defeat me like that. I kept going and trying, despite intense difficulty and heat of the situation. Just do your best, try not to let your anger or frustration defeat you, and stay positive as much as you can. I know its not easy, but its good to try your best here. Good luck, dear friend.