Question
Answer
$$\dfrac{9}{\sqrt{6}+12}=\dfrac{-9\sqrt{6}+108}{138}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{9}{\sqrt{6}+12}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{9}{\sqrt{6}+12}\frac{\sqrt{6}-12}{\sqrt{6}-12} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{9\sqrt{6}-108}{6-12\sqrt{6}+12\sqrt{6}-144} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{9\sqrt{6}-108}{-138} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-9\sqrt{6}+108}{138}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{6}-12} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 9 } \cdot \left( \sqrt{6}-12\right) = \color{blue}{9} \cdot \sqrt{6}+\color{blue}{9} \cdot-12 = \\ = 9 \sqrt{6}-108 $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{6} + 12\right) } \cdot \left( \sqrt{6}-12\right) = \color{blue}{ \sqrt{6}} \cdot \sqrt{6}+\color{blue}{ \sqrt{6}} \cdot-12+\color{blue}{12} \cdot \sqrt{6}+\color{blue}{12} \cdot-12 = \\ = 6- 12 \sqrt{6} + 12 \sqrt{6}-144 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Multiply both numerator and denominator by -1. |
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