Answer
$$\frac{1}{2\sqrt{5}-\sqrt{5}}=\frac{\sqrt{5}}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{1}{2\sqrt{5}-\sqrt{5}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{1}{\sqrt{5}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}} \frac{ 1 }{\sqrt{ 5 }} \times \frac{ \color{orangered}{\sqrt{ 5 }} }{ \color{orangered}{\sqrt{ 5 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{1\sqrt{5}}{5} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\sqrt{5}}{5}\end{aligned} $$ | |
| ① | Simplify numerator and denominator |
| ② | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 5 }}$. |
| ③ | In denominator we have $ \sqrt{ 5 } \cdot \sqrt{ 5 } = 5 $. |
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