Answer
$$\frac{2\sqrt{5}}{\sqrt{6}+\sqrt{6}}=\frac{\sqrt{30}}{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2\sqrt{5}}{\sqrt{6}+\sqrt{6}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2\sqrt{5}}{2\sqrt{6}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{2\sqrt{5}}{2\sqrt{6}}\frac{\sqrt{6}}{\sqrt{6}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{2\sqrt{30}}{12} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{\sqrt{30}}{6}\end{aligned} $$ | |
| ① | Simplify numerator and denominator |
| ② | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{6}} $$. |
| ③ | Multiply in a numerator. $$ \color{blue}{ 2 \sqrt{5} } \cdot \sqrt{6} = 2 \sqrt{30} $$ Simplify denominator. $$ \color{blue}{ 2 \sqrt{6} } \cdot \sqrt{6} = 12 $$ |
| ④ | Divide both numerator and denominator by 2. |
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