Question
Answer
$$\dfrac{9}{5+\sqrt{15}}=\dfrac{45-9\sqrt{15}}{10}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{9}{5+\sqrt{15}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{9}{5+\sqrt{15}}\frac{5-\sqrt{15}}{5-\sqrt{15}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{45-9\sqrt{15}}{25-5\sqrt{15}+5\sqrt{15}-15} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{45-9\sqrt{15}}{10}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 5- \sqrt{15}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 9 } \cdot \left( 5- \sqrt{15}\right) = \color{blue}{9} \cdot5+\color{blue}{9} \cdot- \sqrt{15} = \\ = 45- 9 \sqrt{15} $$ Simplify denominator. $$ \color{blue}{ \left( 5 + \sqrt{15}\right) } \cdot \left( 5- \sqrt{15}\right) = \color{blue}{5} \cdot5+\color{blue}{5} \cdot- \sqrt{15}+\color{blue}{ \sqrt{15}} \cdot5+\color{blue}{ \sqrt{15}} \cdot- \sqrt{15} = \\ = 25- 5 \sqrt{15} + 5 \sqrt{15}-15 $$ |
| ③ | Simplify numerator and denominator |
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