Answer
$$\frac{2\sqrt{3}+3\sqrt{2}}{\sqrt{6}}=\sqrt{2}+\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2\sqrt{3}+3\sqrt{2}}{\sqrt{6}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2\sqrt{3}+3\sqrt{2}}{\sqrt{6}}\frac{\sqrt{6}}{\sqrt{6}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6\sqrt{2}+6\sqrt{3}}{6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{2}+\sqrt{3}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\sqrt{2}+\sqrt{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{6}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 2 \sqrt{3} + 3 \sqrt{2}\right) } \cdot \sqrt{6} = \color{blue}{ 2 \sqrt{3}} \cdot \sqrt{6}+\color{blue}{ 3 \sqrt{2}} \cdot \sqrt{6} = \\ = 6 \sqrt{2} + 6 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ \sqrt{6} } \cdot \sqrt{6} = 6 $$ |
| ③ | Divide both numerator and denominator by 6. |
| ④ | Remove 1 from denominator. |
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