Question
Answer
$$\dfrac{5}{-\sqrt{6}+10}=\dfrac{5\sqrt{6}+50}{94}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5}{-\sqrt{6}+10}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5}{-\sqrt{6}+10}\frac{-\sqrt{6}-10}{-\sqrt{6}-10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-5\sqrt{6}-50}{6+10\sqrt{6}-10\sqrt{6}-100} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-5\sqrt{6}-50}{-94} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{5\sqrt{6}+50}{94}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ - \sqrt{6}-10} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 5 } \cdot \left( - \sqrt{6}-10\right) = \color{blue}{5} \cdot- \sqrt{6}+\color{blue}{5} \cdot-10 = \\ = - 5 \sqrt{6}-50 $$ Simplify denominator. $$ \color{blue}{ \left( - \sqrt{6} + 10\right) } \cdot \left( - \sqrt{6}-10\right) = \color{blue}{- \sqrt{6}} \cdot- \sqrt{6}\color{blue}{- \sqrt{6}} \cdot-10+\color{blue}{10} \cdot- \sqrt{6}+\color{blue}{10} \cdot-10 = \\ = 6 + 10 \sqrt{6}- 10 \sqrt{6}-100 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Multiply both numerator and denominator by -1. |
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