Answer
$$\frac{12\sqrt{2}}{5\sqrt{3}}=\frac{4\sqrt{6}}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{12\sqrt{2}}{5\sqrt{3}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{12\sqrt{2}}{5\sqrt{3}}\frac{\sqrt{3}}{\sqrt{3}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{12\sqrt{6}}{15} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 12 \sqrt{ 6 } : \color{blue}{ 3 } } { 15 : \color{blue}{ 3 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{4\sqrt{6}}{5}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{3}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 12 \sqrt{2} } \cdot \sqrt{3} = 12 \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ 5 \sqrt{3} } \cdot \sqrt{3} = 15 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 3 } $. |
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