Tap the blue circles to see an explanation.
$$ \begin{aligned}\frac{14}{2+\sqrt{3}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{14}{2+\sqrt{3}}\frac{2-\sqrt{3}}{2-\sqrt{3}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{28-14\sqrt{3}}{4-2\sqrt{3}+2\sqrt{3}-3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{28-14\sqrt{3}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}28-14\sqrt{3}\end{aligned} $$ | |
① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 2- \sqrt{3}} $$. |
② | Multiply in a numerator. $$ \color{blue}{ 14 } \cdot \left( 2- \sqrt{3}\right) = \color{blue}{14} \cdot2+\color{blue}{14} \cdot- \sqrt{3} = \\ = 28- 14 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ \left( 2 + \sqrt{3}\right) } \cdot \left( 2- \sqrt{3}\right) = \color{blue}{2} \cdot2+\color{blue}{2} \cdot- \sqrt{3}+\color{blue}{ \sqrt{3}} \cdot2+\color{blue}{ \sqrt{3}} \cdot- \sqrt{3} = \\ = 4- 2 \sqrt{3} + 2 \sqrt{3}-3 $$ |
③ | Simplify numerator and denominator |
④ | Remove 1 from denominator. |