Question
Answer
$$\dfrac{5}{6\sqrt{3}+12}=\dfrac{-30\sqrt{3}+60}{36}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5}{6\sqrt{3}+12}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5}{6\sqrt{3}+12}\frac{6\sqrt{3}-12}{6\sqrt{3}-12} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{30\sqrt{3}-60}{108-72\sqrt{3}+72\sqrt{3}-144} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{30\sqrt{3}-60}{-36} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-30\sqrt{3}+60}{36}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 6 \sqrt{3}-12} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 5 } \cdot \left( 6 \sqrt{3}-12\right) = \color{blue}{5} \cdot 6 \sqrt{3}+\color{blue}{5} \cdot-12 = \\ = 30 \sqrt{3}-60 $$ Simplify denominator. $$ \color{blue}{ \left( 6 \sqrt{3} + 12\right) } \cdot \left( 6 \sqrt{3}-12\right) = \color{blue}{ 6 \sqrt{3}} \cdot 6 \sqrt{3}+\color{blue}{ 6 \sqrt{3}} \cdot-12+\color{blue}{12} \cdot 6 \sqrt{3}+\color{blue}{12} \cdot-12 = \\ = 108- 72 \sqrt{3} + 72 \sqrt{3}-144 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Multiply both numerator and denominator by -1. |
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