Answer
$$\frac{6}{9+\sqrt{13}}=\frac{54-6\sqrt{13}}{68}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{6}{9+\sqrt{13}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{6}{9+\sqrt{13}}\frac{9-\sqrt{13}}{9-\sqrt{13}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{54-6\sqrt{13}}{81-9\sqrt{13}+9\sqrt{13}-13} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{54-6\sqrt{13}}{68}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 9- \sqrt{13}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 6 } \cdot \left( 9- \sqrt{13}\right) = \color{blue}{6} \cdot9+\color{blue}{6} \cdot- \sqrt{13} = \\ = 54- 6 \sqrt{13} $$ Simplify denominator. $$ \color{blue}{ \left( 9 + \sqrt{13}\right) } \cdot \left( 9- \sqrt{13}\right) = \color{blue}{9} \cdot9+\color{blue}{9} \cdot- \sqrt{13}+\color{blue}{ \sqrt{13}} \cdot9+\color{blue}{ \sqrt{13}} \cdot- \sqrt{13} = \\ = 81- 9 \sqrt{13} + 9 \sqrt{13}-13 $$ |
| ③ | Simplify numerator and denominator |
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