Question
Answer
$$\dfrac{-2}{10+\sqrt{6}}=\dfrac{-10+\sqrt{6}}{47}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{-2}{10+\sqrt{6}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{-2}{10+\sqrt{6}}\frac{10-\sqrt{6}}{10-\sqrt{6}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-20+2\sqrt{6}}{100-10\sqrt{6}+10\sqrt{6}-6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-20+2\sqrt{6}}{94} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-10+\sqrt{6}}{47}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 10- \sqrt{6}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ -2 } \cdot \left( 10- \sqrt{6}\right) = \color{blue}{-2} \cdot10\color{blue}{-2} \cdot- \sqrt{6} = \\ = -20 + 2 \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ \left( 10 + \sqrt{6}\right) } \cdot \left( 10- \sqrt{6}\right) = \color{blue}{10} \cdot10+\color{blue}{10} \cdot- \sqrt{6}+\color{blue}{ \sqrt{6}} \cdot10+\color{blue}{ \sqrt{6}} \cdot- \sqrt{6} = \\ = 100- 10 \sqrt{6} + 10 \sqrt{6}-6 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both numerator and denominator by 2. |
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