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