first lets notice that the domain for n is R\{3} since n-3<>0 that is n<>3

n/(n - 3) = 27/24 multiply both sides by 24(n-3) (since LCM(24, (n-3)) = 24(n-3))

24n = 27(n - 3)

24n = 27n - 51

27n - 24n = 51

3n = 51

n = 17 and 17<>3

the value of n is 17.