i used to loose allot vs 3 rax reaper but now i win almost every single time
for me personally i encounter a reaper rush every few tvts and it happens allot
what i do is, at the start of the round place my first supply depot behind behind my gas so and a rax behind my other gas so that reapers cant fly past them(you will need 2 depots but add the second one later)
i do a regular 17 scout and when i see the double gas but no rax, i send it to a spot where it wont get found that is close to his base, and instantly add on a factory second gas, and two bunkers in front of each gas in such a way that my scv line is completely walled off(its ok if there are small gaps by the bunkers but your opponent might try to send the reapers behind the gasses to get too your workers) , and start marine production
even if you think all of what i just said is stupid, the next thing i do kills them almost every time
after my factory finished i add on a tech lab for a tank and instantly build a starport on his side of the map, once the liberator pops he wont be able to mine for possibly minutes and will probably end the game