Hello, eskimogenius!
I have a truly "clunky" approach to the first part . . .
. .
.
We have: .
Long division:
. .
Since the division produces a rational answer, the remainder must be zero.
. .
Therefore: .
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.