Question
Answer
$$\dfrac{2}{-4+\sqrt{15}}=-8-2\sqrt{15}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2}{-4+\sqrt{15}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2}{-4+\sqrt{15}}\frac{-4-\sqrt{15}}{-4-\sqrt{15}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-8-2\sqrt{15}}{16+4\sqrt{15}-4\sqrt{15}-15} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-8-2\sqrt{15}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-8-2\sqrt{15}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ -4- \sqrt{15}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 2 } \cdot \left( -4- \sqrt{15}\right) = \color{blue}{2} \cdot-4+\color{blue}{2} \cdot- \sqrt{15} = \\ = -8- 2 \sqrt{15} $$ Simplify denominator. $$ \color{blue}{ \left( -4 + \sqrt{15}\right) } \cdot \left( -4- \sqrt{15}\right) = \color{blue}{-4} \cdot-4\color{blue}{-4} \cdot- \sqrt{15}+\color{blue}{ \sqrt{15}} \cdot-4+\color{blue}{ \sqrt{15}} \cdot- \sqrt{15} = \\ = 16 + 4 \sqrt{15}- 4 \sqrt{15}-15 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Remove 1 from denominator. |
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