Answer
$$\frac{48}{5+\sqrt{13}}=\frac{240-48\sqrt{13}}{12}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{48}{5+\sqrt{13}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{48}{5+\sqrt{13}}\frac{5-\sqrt{13}}{5-\sqrt{13}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{240-48\sqrt{13}}{25-5\sqrt{13}+5\sqrt{13}-13} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{240-48\sqrt{13}}{12}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 5- \sqrt{13}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 48 } \cdot \left( 5- \sqrt{13}\right) = \color{blue}{48} \cdot5+\color{blue}{48} \cdot- \sqrt{13} = \\ = 240- 48 \sqrt{13} $$ Simplify denominator. $$ \color{blue}{ \left( 5 + \sqrt{13}\right) } \cdot \left( 5- \sqrt{13}\right) = \color{blue}{5} \cdot5+\color{blue}{5} \cdot- \sqrt{13}+\color{blue}{ \sqrt{13}} \cdot5+\color{blue}{ \sqrt{13}} \cdot- \sqrt{13} = \\ = 25- 5 \sqrt{13} + 5 \sqrt{13}-13 $$ |
| ③ | Simplify numerator and denominator |
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