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