Question
Answer
$$\dfrac{11\sqrt{13}}{11-\sqrt{13}}=\dfrac{121\sqrt{13}+143}{108}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{11\sqrt{13}}{11-\sqrt{13}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{11\sqrt{13}}{11-\sqrt{13}}\frac{11+\sqrt{13}}{11+\sqrt{13}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{121\sqrt{13}+143}{121+11\sqrt{13}-11\sqrt{13}-13} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{121\sqrt{13}+143}{108}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 11 + \sqrt{13}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 11 \sqrt{13} } \cdot \left( 11 + \sqrt{13}\right) = \color{blue}{ 11 \sqrt{13}} \cdot11+\color{blue}{ 11 \sqrt{13}} \cdot \sqrt{13} = \\ = 121 \sqrt{13} + 143 $$ Simplify denominator. $$ \color{blue}{ \left( 11- \sqrt{13}\right) } \cdot \left( 11 + \sqrt{13}\right) = \color{blue}{11} \cdot11+\color{blue}{11} \cdot \sqrt{13}\color{blue}{- \sqrt{13}} \cdot11\color{blue}{- \sqrt{13}} \cdot \sqrt{13} = \\ = 121 + 11 \sqrt{13}- 11 \sqrt{13}-13 $$ |
| ③ | Simplify numerator and denominator |
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