The average of x numbers is y and average of y numbers is x. Then the average of all the numbers taken together is:
[A] $\frac{xy}{x+y}$
[B] $\frac{x+y}{2xy}$
[C] $\frac{x^{2}+y^{2}}{x+y}$
[D] $\frac{2xy}{x+y}$