X~Gamma(theta,alpha)

y~Gamma(theta,beta)

U=X/Y

V=X+Y

Find fX,Y(x,y)

State whether U and V are independent

Find marginal pdf

i am having trouble finding fX,Y(x,y) using information given that X and Y are of Gamma distribution.

And what is the theorem used to determine the independence of U and V?