Question
Answer
$$\dfrac{8}{\sqrt{7}-\sqrt{11}}=-\dfrac{8\sqrt{7}+8\sqrt{11}}{4}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{8}{\sqrt{7}-\sqrt{11}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{8}{\sqrt{7}-\sqrt{11}}\frac{\sqrt{7}+\sqrt{11}}{\sqrt{7}+\sqrt{11}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{8\sqrt{7}+8\sqrt{11}}{7+\sqrt{77}-\sqrt{77}-11} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{8\sqrt{7}+8\sqrt{11}}{-4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-\frac{8\sqrt{7}+8\sqrt{11}}{4}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{7} + \sqrt{11}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 8 } \cdot \left( \sqrt{7} + \sqrt{11}\right) = \color{blue}{8} \cdot \sqrt{7}+\color{blue}{8} \cdot \sqrt{11} = \\ = 8 \sqrt{7} + 8 \sqrt{11} $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{7}- \sqrt{11}\right) } \cdot \left( \sqrt{7} + \sqrt{11}\right) = \color{blue}{ \sqrt{7}} \cdot \sqrt{7}+\color{blue}{ \sqrt{7}} \cdot \sqrt{11}\color{blue}{- \sqrt{11}} \cdot \sqrt{7}\color{blue}{- \sqrt{11}} \cdot \sqrt{11} = \\ = 7 + \sqrt{77}- \sqrt{77}-11 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Place a negative sign in front of a fraction. |
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