Answer
$$\frac{2}{\sqrt{3}+2\sqrt{4}}=\frac{-2\sqrt{3}+8}{13}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2}{\sqrt{3}+2\sqrt{4}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2}{\sqrt{3}+2\sqrt{4}}\frac{\sqrt{3}-2\sqrt{4}}{\sqrt{3}-2\sqrt{4}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{2\sqrt{3}-8}{3-4\sqrt{3}+4\sqrt{3}-16} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{2\sqrt{3}-8}{-13} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-2\sqrt{3}+8}{13}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{3}- 2 \sqrt{4}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 2 } \cdot \left( \sqrt{3}- 2 \sqrt{4}\right) = \color{blue}{2} \cdot \sqrt{3}+\color{blue}{2} \cdot- 2 \sqrt{4} = \\ = 2 \sqrt{3}-8 $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{3} + 2 \sqrt{4}\right) } \cdot \left( \sqrt{3}- 2 \sqrt{4}\right) = \color{blue}{ \sqrt{3}} \cdot \sqrt{3}+\color{blue}{ \sqrt{3}} \cdot- 2 \sqrt{4}+\color{blue}{ 2 \sqrt{4}} \cdot \sqrt{3}+\color{blue}{ 2 \sqrt{4}} \cdot- 2 \sqrt{4} = \\ = 3- 4 \sqrt{3} + 4 \sqrt{3}-16 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Multiply both numerator and denominator by -1. |
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