stable state of two separate queues and of merging queue

Question

if $n_{1}(t)$ is the total number of demands in two independent and similar $M/M/1$ queue with demand entry rate $\lambda$ and service rate $\mu$, how can I prove that the probability of stable states are: $$p(n_{1}(t)=n) = (n+1)(1-\rho)^2 .\rho ^n$$ that $n\ge0$ and $\rho=\lambda / \mu$. and if we merge two queues and make a $M/M/2$ queue, how can I prove that in stable state : $$p(n_{2}(t)=n) =(2(1-\rho)(\rho)^n)/(1+\rho)$$ if $n\ge0$ and $$p(n_{2}(t)=n) = (1-\rho)/(1+\rho)$$ if $n=0 $. thanks a lot.