Question
Answer
$$\dfrac{8}{-6+\sqrt{15}}=\dfrac{-48-8\sqrt{15}}{21}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{8}{-6+\sqrt{15}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{8}{-6+\sqrt{15}}\frac{-6-\sqrt{15}}{-6-\sqrt{15}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-48-8\sqrt{15}}{36+6\sqrt{15}-6\sqrt{15}-15} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-48-8\sqrt{15}}{21}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ -6- \sqrt{15}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 8 } \cdot \left( -6- \sqrt{15}\right) = \color{blue}{8} \cdot-6+\color{blue}{8} \cdot- \sqrt{15} = \\ = -48- 8 \sqrt{15} $$ Simplify denominator. $$ \color{blue}{ \left( -6 + \sqrt{15}\right) } \cdot \left( -6- \sqrt{15}\right) = \color{blue}{-6} \cdot-6\color{blue}{-6} \cdot- \sqrt{15}+\color{blue}{ \sqrt{15}} \cdot-6+\color{blue}{ \sqrt{15}} \cdot- \sqrt{15} = \\ = 36 + 6 \sqrt{15}- 6 \sqrt{15}-15 $$ |
| ③ | Simplify numerator and denominator |
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