Answer
$$\frac{2}{9-\sqrt{6}}=\frac{18+2\sqrt{6}}{75}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2}{9-\sqrt{6}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2}{9-\sqrt{6}}\frac{9+\sqrt{6}}{9+\sqrt{6}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{18+2\sqrt{6}}{81+9\sqrt{6}-9\sqrt{6}-6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{18+2\sqrt{6}}{75}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 9 + \sqrt{6}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 2 } \cdot \left( 9 + \sqrt{6}\right) = \color{blue}{2} \cdot9+\color{blue}{2} \cdot \sqrt{6} = \\ = 18 + 2 \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ \left( 9- \sqrt{6}\right) } \cdot \left( 9 + \sqrt{6}\right) = \color{blue}{9} \cdot9+\color{blue}{9} \cdot \sqrt{6}\color{blue}{- \sqrt{6}} \cdot9\color{blue}{- \sqrt{6}} \cdot \sqrt{6} = \\ = 81 + 9 \sqrt{6}- 9 \sqrt{6}-6 $$ |
| ③ | Simplify numerator and denominator |
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