Question
Answer
$$\dfrac{5}{\sqrt{12}-3}=\dfrac{10\sqrt{3}+15}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5}{\sqrt{12}-3}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5}{\sqrt{12}-3}\frac{\sqrt{12}+3}{\sqrt{12}+3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{10\sqrt{3}+15}{12+6\sqrt{3}-6\sqrt{3}-9} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{10\sqrt{3}+15}{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{12} + 3} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 5 } \cdot \left( \sqrt{12} + 3\right) = \color{blue}{5} \cdot \sqrt{12}+\color{blue}{5} \cdot3 = \\ = 10 \sqrt{3} + 15 $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{12}-3\right) } \cdot \left( \sqrt{12} + 3\right) = \color{blue}{ \sqrt{12}} \cdot \sqrt{12}+\color{blue}{ \sqrt{12}} \cdot3\color{blue}{-3} \cdot \sqrt{12}\color{blue}{-3} \cdot3 = \\ = 12 + 6 \sqrt{3}- 6 \sqrt{3}-9 $$ |
| ③ | Simplify numerator and denominator |
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