Question
Answer
$$\dfrac{2\sqrt{3}-\sqrt{5}}{2\sqrt{3}+3\sqrt{3}}=\dfrac{6-\sqrt{15}}{15}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2\sqrt{3}-\sqrt{5}}{2\sqrt{3}+3\sqrt{3}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2\sqrt{3}-\sqrt{5}}{5\sqrt{3}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{2\sqrt{3}-\sqrt{5}}{5\sqrt{3}}\frac{\sqrt{3}}{\sqrt{3}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{6-\sqrt{15}}{15}\end{aligned} $$ | |
| ① | Simplify numerator and denominator |
| ② | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{3}} $$. |
| ③ | Multiply in a numerator. $$ \color{blue}{ \left( 2 \sqrt{3}- \sqrt{5}\right) } \cdot \sqrt{3} = \color{blue}{ 2 \sqrt{3}} \cdot \sqrt{3}\color{blue}{- \sqrt{5}} \cdot \sqrt{3} = \\ = 6- \sqrt{15} $$ Simplify denominator. $$ \color{blue}{ 5 \sqrt{3} } \cdot \sqrt{3} = 15 $$ |
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