I have a truly "clunky" approach to the first part . . .
We have: .
Since the division produces a rational answer, the remainder must be zero.
Never mind about that second part, my math teacher has solved it. Thank you very much Soroban.
For those who want to know the solution:
The first fraction that was given when compared to the second fraction: it can be seen that b = 1. Now for it to be true, the above proven equation has to hold.
When you sub b=1 into the proven equation above, it can be seen that
However, as a, c and d are positive integers, that fraction has to be less than one, and hence this is impossible because c is a positive integer.
Therefore, the second fraction is never rational.
PS. By fraction I mean everything that is need to be proved irrational and everything that is need to be proved irrational.