2012 AIME II Problem 9

Let x and y be real numbers such that \frac{\sin x}{\sin y}=3 and \frac{\cos x}{\cos y}=\frac{1}{2}. The value of \frac{\sin 2 x}{\sin 2 y}+\frac{\cos 2 x}{\cos 2 y} can be expressed in the form \frac{p}{q}, where p and q are relatively prime positive integers. Find p+q.