Question
Answer
$$\dfrac{2}{\sqrt{7}-6}=-\dfrac{2\sqrt{7}+12}{29}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2}{\sqrt{7}-6}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2}{\sqrt{7}-6}\frac{\sqrt{7}+6}{\sqrt{7}+6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{2\sqrt{7}+12}{7+6\sqrt{7}-6\sqrt{7}-36} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{2\sqrt{7}+12}{-29} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-\frac{2\sqrt{7}+12}{29}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{7} + 6} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 2 } \cdot \left( \sqrt{7} + 6\right) = \color{blue}{2} \cdot \sqrt{7}+\color{blue}{2} \cdot6 = \\ = 2 \sqrt{7} + 12 $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{7}-6\right) } \cdot \left( \sqrt{7} + 6\right) = \color{blue}{ \sqrt{7}} \cdot \sqrt{7}+\color{blue}{ \sqrt{7}} \cdot6\color{blue}{-6} \cdot \sqrt{7}\color{blue}{-6} \cdot6 = \\ = 7 + 6 \sqrt{7}- 6 \sqrt{7}-36 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Place a negative sign in front of a fraction. |
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