Q13/044) N and M are positive integers such that N+M=21. The largest possible value of 1/N+1/M is a/b ( and b are co-primes) .Find a+b

1/N+1/M = (N+M)/NM = 21/(NM)
This is largest when NM is lowest.
clearly when N= 1 and M= 20 ( or N = 20, M = 1)
so NM = 20
so a= 21 and b = 20 hence a+b = 41