Question
Answer
$$\dfrac{-9}{\sqrt{2}+\sqrt{2}\cdot1}=\dfrac{-9\sqrt{2}}{4}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{-9}{\sqrt{2}+\sqrt{2}\cdot1}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{-9}{2\sqrt{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-9}{2\sqrt{2}}\frac{\sqrt{2}}{\sqrt{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-9\sqrt{2}}{4}\end{aligned} $$ | |
| ① | Simplify numerator and denominator |
| ② | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{2}} $$. |
| ③ | Multiply in a numerator. $$ \color{blue}{ -9 } \cdot \sqrt{2} = - 9 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ 2 \sqrt{2} } \cdot \sqrt{2} = 4 $$ |
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