Covariance of two sample means

Hello all!

I am looking to calculate VAR(xbar-ybar) where X and Y are not independent.

Want to try VAR(xbar) +VAR(ybar)+2COV(xbar,ybar).

I know VAR(xbar) = sigma^2 of X / n1

I know VAR(ybar) = sigma^2 of Y / n2

But the COV(xbar,ybar) has me stumped. I wanted to write

(1/n1)* (1/n2) * COV (SUM(Xi) 1 to n1, SUM(Yi) 1 to n2).

I have researched the additive rule of COV(X+Y,Z) = COV(X,Y) + COV(Y,Z) but not sure how to apply with a sum in both 'places' for COV(X,Y).

Anyone help?

Thanks!