Let . Then show that x is an integer. (Hint: First show that x is a rational number)
is an integer
is also an integer.
Hence ratio of those two are is a rational.
Again are rational. Also it is given that is integer. Hence is rational.
Therefore is rational. Since ratio of rationals is rational.
Suppose x = p/q, then where gcd(p, q) = 1 and k is an integer.
But this implies q divides p which means q = 1.
Hence x is an integer. (Proved)