Question
Answer
$$\dfrac{6}{\sqrt{8}-8}=-\dfrac{12\sqrt{2}+48}{56}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{6}{\sqrt{8}-8}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{6}{\sqrt{8}-8}\frac{\sqrt{8}+8}{\sqrt{8}+8} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{12\sqrt{2}+48}{8+16\sqrt{2}-16\sqrt{2}-64} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{12\sqrt{2}+48}{-56} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-\frac{12\sqrt{2}+48}{56}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{8} + 8} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 6 } \cdot \left( \sqrt{8} + 8\right) = \color{blue}{6} \cdot \sqrt{8}+\color{blue}{6} \cdot8 = \\ = 12 \sqrt{2} + 48 $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{8}-8\right) } \cdot \left( \sqrt{8} + 8\right) = \color{blue}{ \sqrt{8}} \cdot \sqrt{8}+\color{blue}{ \sqrt{8}} \cdot8\color{blue}{-8} \cdot \sqrt{8}\color{blue}{-8} \cdot8 = \\ = 8 + 16 \sqrt{2}- 16 \sqrt{2}-64 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Place a negative sign in front of a fraction. |
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