Question
Answer
$$\dfrac{12}{\sqrt{7}-\sqrt{13}}=-\dfrac{12\sqrt{7}+12\sqrt{13}}{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{12}{\sqrt{7}-\sqrt{13}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{12}{\sqrt{7}-\sqrt{13}}\frac{\sqrt{7}+\sqrt{13}}{\sqrt{7}+\sqrt{13}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{12\sqrt{7}+12\sqrt{13}}{7+\sqrt{91}-\sqrt{91}-13} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{12\sqrt{7}+12\sqrt{13}}{-6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-\frac{12\sqrt{7}+12\sqrt{13}}{6}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{7} + \sqrt{13}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 12 } \cdot \left( \sqrt{7} + \sqrt{13}\right) = \color{blue}{12} \cdot \sqrt{7}+\color{blue}{12} \cdot \sqrt{13} = \\ = 12 \sqrt{7} + 12 \sqrt{13} $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{7}- \sqrt{13}\right) } \cdot \left( \sqrt{7} + \sqrt{13}\right) = \color{blue}{ \sqrt{7}} \cdot \sqrt{7}+\color{blue}{ \sqrt{7}} \cdot \sqrt{13}\color{blue}{- \sqrt{13}} \cdot \sqrt{7}\color{blue}{- \sqrt{13}} \cdot \sqrt{13} = \\ = 7 + \sqrt{91}- \sqrt{91}-13 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Place a negative sign in front of a fraction. |
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