Use Binet's formula to show that

$\displaystyle \frac{f_n+1}{f_n} = \frac{1+\sqrt{5}}{2} $. I know that Binet's formula is

$\displaystyle f_n= \frac{(1+ \sqrt{5})^n-(1- \sqrt{5})^n}{(2^n)\sqrt{5}} $

So, when I substitute, I get down to

$\displaystyle f_n= \frac{(1+ \sqrt{5})^{n+1}-(1- \sqrt{5})^{n+1}}{(1+ \sqrt{5})^{n}-(1- \sqrt{5})^n(2^n)\sqrt{5}} $

but I am not sure how to simpify this equation. I know that the answer is

$\displaystyle \frac{1+ \sqrt{5}}{2}$.