Answer
$$\frac{\sqrt{12}-\sqrt{6}}{\sqrt{24}}=\frac{\sqrt{2}-1}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{12}-\sqrt{6}}{\sqrt{24}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{12}-\sqrt{6}}{\sqrt{24}}\frac{\sqrt{24}}{\sqrt{24}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{12\sqrt{2}-12}{24} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{2}-1}{2}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{24}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( \sqrt{12}- \sqrt{6}\right) } \cdot \sqrt{24} = \color{blue}{ \sqrt{12}} \cdot \sqrt{24}\color{blue}{- \sqrt{6}} \cdot \sqrt{24} = \\ = 12 \sqrt{2}-12 $$ Simplify denominator. $$ \color{blue}{ \sqrt{24} } \cdot \sqrt{24} = 24 $$ |
| ③ | Divide both numerator and denominator by 12. |
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