Question
Answer
$$\dfrac{6}{-\sqrt{15}+\sqrt{6}}=\dfrac{-6\sqrt{15}-6\sqrt{6}}{9}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{6}{-\sqrt{15}+\sqrt{6}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{6}{-\sqrt{15}+\sqrt{6}}\frac{-\sqrt{15}-\sqrt{6}}{-\sqrt{15}-\sqrt{6}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-6\sqrt{15}-6\sqrt{6}}{15+3\sqrt{10}-3\sqrt{10}-6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-6\sqrt{15}-6\sqrt{6}}{9}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ - \sqrt{15}- \sqrt{6}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 6 } \cdot \left( - \sqrt{15}- \sqrt{6}\right) = \color{blue}{6} \cdot- \sqrt{15}+\color{blue}{6} \cdot- \sqrt{6} = \\ = - 6 \sqrt{15}- 6 \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ \left( - \sqrt{15} + \sqrt{6}\right) } \cdot \left( - \sqrt{15}- \sqrt{6}\right) = \color{blue}{- \sqrt{15}} \cdot- \sqrt{15}\color{blue}{- \sqrt{15}} \cdot- \sqrt{6}+\color{blue}{ \sqrt{6}} \cdot- \sqrt{15}+\color{blue}{ \sqrt{6}} \cdot- \sqrt{6} = \\ = 15 + 3 \sqrt{10}- 3 \sqrt{10}-6 $$ |
| ③ | Simplify numerator and denominator |
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