Difficult question

for all natural number n,

By Euckidean Algorithm,

1| 21n+4 | 14n+3 | 2
- | 14n+3 | 14n+2 |
-----------------------------------------
. | 7n+1 | 1 |

therefore,the greatest common factor of 21n+4 and 14n+3 is 1
=>21n+4 and 14n+3 are relatively prime
=>(21n+4)/(14n+3) is the fraction in the simplest form