Hey akolman.

Recall that the Moment Generating Function of a variable Y is E[e^(tY)] and in this case Y=X/Z and the expectation of E[X/Z] = Integral (over whole of R^2) (x/z)*f(x,z)dxdz.

The characteristic function of a random variable is simply MGF_Y(it) where MGF_Y(t) = E[e^(tY)] so the characteristic function is simply E[e^(itY)].

To start, setup your integral and see how you go.