Answer
$$\frac{12}{\sqrt{13}-\sqrt{10}}=\frac{12\sqrt{13}+12\sqrt{10}}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{12}{\sqrt{13}-\sqrt{10}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{12}{\sqrt{13}-\sqrt{10}}\frac{\sqrt{13}+\sqrt{10}}{\sqrt{13}+\sqrt{10}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{12\sqrt{13}+12\sqrt{10}}{13+\sqrt{130}-\sqrt{130}-10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{12\sqrt{13}+12\sqrt{10}}{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{13} + \sqrt{10}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 12 } \cdot \left( \sqrt{13} + \sqrt{10}\right) = \color{blue}{12} \cdot \sqrt{13}+\color{blue}{12} \cdot \sqrt{10} = \\ = 12 \sqrt{13} + 12 \sqrt{10} $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{13}- \sqrt{10}\right) } \cdot \left( \sqrt{13} + \sqrt{10}\right) = \color{blue}{ \sqrt{13}} \cdot \sqrt{13}+\color{blue}{ \sqrt{13}} \cdot \sqrt{10}\color{blue}{- \sqrt{10}} \cdot \sqrt{13}\color{blue}{- \sqrt{10}} \cdot \sqrt{10} = \\ = 13 + \sqrt{130}- \sqrt{130}-10 $$ |
| ③ | Simplify numerator and denominator |
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