Answer
$$\frac{6}{\sqrt{26}-2}=\frac{6\sqrt{26}+12}{22}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{6}{\sqrt{26}-2}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{6}{\sqrt{26}-2}\frac{\sqrt{26}+2}{\sqrt{26}+2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6\sqrt{26}+12}{26+2\sqrt{26}-2\sqrt{26}-4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{6\sqrt{26}+12}{22}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{26} + 2} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 6 } \cdot \left( \sqrt{26} + 2\right) = \color{blue}{6} \cdot \sqrt{26}+\color{blue}{6} \cdot2 = \\ = 6 \sqrt{26} + 12 $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{26}-2\right) } \cdot \left( \sqrt{26} + 2\right) = \color{blue}{ \sqrt{26}} \cdot \sqrt{26}+\color{blue}{ \sqrt{26}} \cdot2\color{blue}{-2} \cdot \sqrt{26}\color{blue}{-2} \cdot2 = \\ = 26 + 2 \sqrt{26}- 2 \sqrt{26}-4 $$ |
| ③ | Simplify numerator and denominator |
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