Question
Answer
$$\dfrac{6}{-7+\sqrt{6}}=\dfrac{-42-6\sqrt{6}}{43}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{6}{-7+\sqrt{6}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{6}{-7+\sqrt{6}}\frac{-7-\sqrt{6}}{-7-\sqrt{6}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-42-6\sqrt{6}}{49+7\sqrt{6}-7\sqrt{6}-6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-42-6\sqrt{6}}{43}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ -7- \sqrt{6}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 6 } \cdot \left( -7- \sqrt{6}\right) = \color{blue}{6} \cdot-7+\color{blue}{6} \cdot- \sqrt{6} = \\ = -42- 6 \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ \left( -7 + \sqrt{6}\right) } \cdot \left( -7- \sqrt{6}\right) = \color{blue}{-7} \cdot-7\color{blue}{-7} \cdot- \sqrt{6}+\color{blue}{ \sqrt{6}} \cdot-7+\color{blue}{ \sqrt{6}} \cdot- \sqrt{6} = \\ = 49 + 7 \sqrt{6}- 7 \sqrt{6}-6 $$ |
| ③ | Simplify numerator and denominator |
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