Denote the Hirsch length of a group $G$ by $h(G)$. Let $G$ be a virtually polycyclic group and let $H$ be a normal subgroup of $G$. I am not sure how to prove that $h(G)=h(G/H)+h(H)$.
I know the above relation is quite trivial in the polycyclic case, but I do not know how to deal with the virtually polycyclic case. I hope someone can help me.