Answer
$$\frac{5}{4\sqrt{3}-4}=\frac{20\sqrt{3}+20}{32}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5}{4\sqrt{3}-4}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5}{4\sqrt{3}-4}\frac{4\sqrt{3}+4}{4\sqrt{3}+4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{20\sqrt{3}+20}{48+16\sqrt{3}-16\sqrt{3}-16} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{20\sqrt{3}+20}{32}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 4 \sqrt{3} + 4} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 5 } \cdot \left( 4 \sqrt{3} + 4\right) = \color{blue}{5} \cdot 4 \sqrt{3}+\color{blue}{5} \cdot4 = \\ = 20 \sqrt{3} + 20 $$ Simplify denominator. $$ \color{blue}{ \left( 4 \sqrt{3}-4\right) } \cdot \left( 4 \sqrt{3} + 4\right) = \color{blue}{ 4 \sqrt{3}} \cdot 4 \sqrt{3}+\color{blue}{ 4 \sqrt{3}} \cdot4\color{blue}{-4} \cdot 4 \sqrt{3}\color{blue}{-4} \cdot4 = \\ = 48 + 16 \sqrt{3}- 16 \sqrt{3}-16 $$ |
| ③ | Simplify numerator and denominator |
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