Answer
$$\frac{\sqrt{14}-\sqrt{3}}{2\sqrt{3}}=\frac{\sqrt{42}-3}{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{14}-\sqrt{3}}{2\sqrt{3}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{14}-\sqrt{3}}{2\sqrt{3}}\frac{\sqrt{3}}{\sqrt{3}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{\sqrt{42}-3}{6}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{3}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( \sqrt{14}- \sqrt{3}\right) } \cdot \sqrt{3} = \color{blue}{ \sqrt{14}} \cdot \sqrt{3}\color{blue}{- \sqrt{3}} \cdot \sqrt{3} = \\ = \sqrt{42}-3 $$ Simplify denominator. $$ \color{blue}{ 2 \sqrt{3} } \cdot \sqrt{3} = 6 $$ |
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