For Z distributed on R^3 with Z1, Z2, Z3 IID Z ~ exp(1)

I have X = (Z2 + Z3)/(Z1 + Z2 + Z3)

How can i determine the distribution of X and obtain its mean and variance?

I was thinking perhaps I need to do something in terms of gamma because standard exponential is z ~ exp(1) iff z ~ G(1) and chi-square possibly???

plz someone can help me??