Tap the blue circles to see an explanation.
$$ \begin{aligned}\frac{\sqrt{3}}{\sqrt{2}+3}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{3}}{\sqrt{2}+3}\frac{\sqrt{2}-3}{\sqrt{2}-3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{\sqrt{6}-3\sqrt{3}}{2-3\sqrt{2}+3\sqrt{2}-9} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{6}-3\sqrt{3}}{-7} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-\sqrt{6}+3\sqrt{3}}{7}\end{aligned} $$ | |
① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{2}-3} $$. |
② | Multiply in a numerator. $$ \color{blue}{ \sqrt{3} } \cdot \left( \sqrt{2}-3\right) = \color{blue}{ \sqrt{3}} \cdot \sqrt{2}+\color{blue}{ \sqrt{3}} \cdot-3 = \\ = \sqrt{6}- 3 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{2} + 3\right) } \cdot \left( \sqrt{2}-3\right) = \color{blue}{ \sqrt{2}} \cdot \sqrt{2}+\color{blue}{ \sqrt{2}} \cdot-3+\color{blue}{3} \cdot \sqrt{2}+\color{blue}{3} \cdot-3 = \\ = 2- 3 \sqrt{2} + 3 \sqrt{2}-9 $$ |
③ | Simplify numerator and denominator |
④ | Multiply both numerator and denominator by -1. |