Fibonacci Limit II

Let $F_n$ be the Fibonacci sequence. Compute $\displaystyle \lim_{n \rightarrow \infty} \dfrac{F_{n+2}}{F_n}$. Your answer should be in the form $\dfrac{a+\sqrt{b}}{c}$, where all of $a,b,$ and $c$ are pairwise relatively prime. Find $abc$.