X is a positive rational number greater than 1. If the two integers that make up the ratio are both positive, then the numerator must be greater than the denominator for the value of the ratio to be greater than 1.
So now let's look at subtracting the numerator and the denominator. We know that p > q and they are both positive integers.
So, p - q must be a positive integer greater than 1 because it is a positive integer subtracted by a smaller positive integer.