Question
Answer
$$\dfrac{2}{-4+3\sqrt{6}}=\dfrac{4+3\sqrt{6}}{19}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2}{-4+3\sqrt{6}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2}{-4+3\sqrt{6}}\frac{-4-3\sqrt{6}}{-4-3\sqrt{6}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-8-6\sqrt{6}}{16+12\sqrt{6}-12\sqrt{6}-54} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-8-6\sqrt{6}}{-38} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-4-3\sqrt{6}}{-19} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{4+3\sqrt{6}}{19}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ -4- 3 \sqrt{6}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 2 } \cdot \left( -4- 3 \sqrt{6}\right) = \color{blue}{2} \cdot-4+\color{blue}{2} \cdot- 3 \sqrt{6} = \\ = -8- 6 \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ \left( -4 + 3 \sqrt{6}\right) } \cdot \left( -4- 3 \sqrt{6}\right) = \color{blue}{-4} \cdot-4\color{blue}{-4} \cdot- 3 \sqrt{6}+\color{blue}{ 3 \sqrt{6}} \cdot-4+\color{blue}{ 3 \sqrt{6}} \cdot- 3 \sqrt{6} = \\ = 16 + 12 \sqrt{6}- 12 \sqrt{6}-54 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both numerator and denominator by 2. |
| ⑤ | Multiply both numerator and denominator by -1. |
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