Answer
$$\frac{-2}{-10-\sqrt{13}}=\frac{20-2\sqrt{13}}{87}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{-2}{-10-\sqrt{13}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{-2}{-10-\sqrt{13}}\frac{-10+\sqrt{13}}{-10+\sqrt{13}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{20-2\sqrt{13}}{100-10\sqrt{13}+10\sqrt{13}-13} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{20-2\sqrt{13}}{87}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ -10 + \sqrt{13}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ -2 } \cdot \left( -10 + \sqrt{13}\right) = \color{blue}{-2} \cdot-10\color{blue}{-2} \cdot \sqrt{13} = \\ = 20- 2 \sqrt{13} $$ Simplify denominator. $$ \color{blue}{ \left( -10- \sqrt{13}\right) } \cdot \left( -10 + \sqrt{13}\right) = \color{blue}{-10} \cdot-10\color{blue}{-10} \cdot \sqrt{13}\color{blue}{- \sqrt{13}} \cdot-10\color{blue}{- \sqrt{13}} \cdot \sqrt{13} = \\ = 100- 10 \sqrt{13} + 10 \sqrt{13}-13 $$ |
| ③ | Simplify numerator and denominator |
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