Answer
$$\frac{\sqrt{11}}{\sqrt{11}-2}=\frac{11+2\sqrt{11}}{7}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{11}}{\sqrt{11}-2}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{11}}{\sqrt{11}-2}\frac{\sqrt{11}+2}{\sqrt{11}+2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{11+2\sqrt{11}}{11+2\sqrt{11}-2\sqrt{11}-4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{11+2\sqrt{11}}{7}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{11} + 2} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \sqrt{11} } \cdot \left( \sqrt{11} + 2\right) = \color{blue}{ \sqrt{11}} \cdot \sqrt{11}+\color{blue}{ \sqrt{11}} \cdot2 = \\ = 11 + 2 \sqrt{11} $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{11}-2\right) } \cdot \left( \sqrt{11} + 2\right) = \color{blue}{ \sqrt{11}} \cdot \sqrt{11}+\color{blue}{ \sqrt{11}} \cdot2\color{blue}{-2} \cdot \sqrt{11}\color{blue}{-2} \cdot2 = \\ = 11 + 2 \sqrt{11}- 2 \sqrt{11}-4 $$ |
| ③ | Simplify numerator and denominator |
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