Question
Answer
$$\dfrac{5}{4\sqrt{3}+4}=\dfrac{20\sqrt{3}-20}{32}$$
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. $$ \color{blue}{ 5 } \cdot \left( 4 \sqrt{3}-4\right) = \color{blue}{5} \cdot 4 \sqrt{3}+\color{blue}{5} \cdot-4 = \\ = 20 \sqrt{3}-20 $$ Simplify denominator. $$ \color{blue}{ \left( 4 \sqrt{3} + 4\right) } \cdot \left( 4 \sqrt{3}-4\right) = \color{blue}{ 4 \sqrt{3}} \cdot 4 \sqrt{3}+\color{blue}{ 4 \sqrt{3}} \cdot-4+\color{blue}{4} \cdot 4 \sqrt{3}+\color{blue}{4} \cdot-4 = \\ = 48- 16 \sqrt{3} + 16 \sqrt{3}-16 $$ |
| ③ | Simplify numerator and denominator |
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