Question
Answer
$$\dfrac{-9}{\sqrt{6}+\sqrt{10}}=\dfrac{9\sqrt{6}-9\sqrt{10}}{4}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{-9}{\sqrt{6}+\sqrt{10}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{-9}{\sqrt{6}+\sqrt{10}}\frac{\sqrt{6}-\sqrt{10}}{\sqrt{6}-\sqrt{10}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-9\sqrt{6}+9\sqrt{10}}{6-2\sqrt{15}+2\sqrt{15}-10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-9\sqrt{6}+9\sqrt{10}}{-4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{9\sqrt{6}-9\sqrt{10}}{4}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{6}- \sqrt{10}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ -9 } \cdot \left( \sqrt{6}- \sqrt{10}\right) = \color{blue}{-9} \cdot \sqrt{6}\color{blue}{-9} \cdot- \sqrt{10} = \\ = - 9 \sqrt{6} + 9 \sqrt{10} $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{6} + \sqrt{10}\right) } \cdot \left( \sqrt{6}- \sqrt{10}\right) = \color{blue}{ \sqrt{6}} \cdot \sqrt{6}+\color{blue}{ \sqrt{6}} \cdot- \sqrt{10}+\color{blue}{ \sqrt{10}} \cdot \sqrt{6}+\color{blue}{ \sqrt{10}} \cdot- \sqrt{10} = \\ = 6- 2 \sqrt{15} + 2 \sqrt{15}-10 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Multiply both numerator and denominator by -1. |
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