Answer
$$\frac{4+\sqrt{5}+4-\sqrt{5}}{4-\sqrt{5}+4+\sqrt{5}}=1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4+\sqrt{5}+4-\sqrt{5}}{4-\sqrt{5}+4+\sqrt{5}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{8}{8} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}} \frac{ 8 : \color{orangered}{ 8 } }{ 8 : \color{orangered}{ 8 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{1}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}1\end{aligned} $$ | |
| ① | Simplify numerator and denominator |
| ② | Divide both the top and bottom numbers by $ \color{orangered}{ 8 } $. |
| ③ | Remove 1 from denominator. |
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