a_n=\frac{-n+\sqrt{n(n+2)}}{{n+2-\sqrt{n(n+2}}}
a_n=\frac{[-n+\sqrt{n(n+2)}]*[n+2+\sqrt{n(n+2)}]}{[{n+2-\sqrt{n(n+2}]*[n+2+\sqrt{n(n+2}]}}
a_n=\frac{-n(n+2)-n\sqrt{n(n+2}+(n+2)\sqrt{n(n+2}+n(n+2)}{{(n+2)^2}-n(n+2)}
a_n=\frac{2\sqrt{n(n+2}}{(n+2)[n+2-n]}=\frac{2\sqrt{n(n+2}}{2(n+2)}=\sqrt{\frac{n(n+2)}{(n+2)^2}}=\sqrt{\frac{n}{n+2}}
\lim{a_n}=1