Answer
$$\frac{\frac{1}{\sqrt{2}}}{1-\frac{1}{\sqrt{2}}}=\frac{\frac{\sqrt{2}}{2}}{1-\frac{1}{\sqrt{2}}}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\frac{1}{\sqrt{2}}}{1-\frac{1}{\sqrt{2}}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{ \frac{ 1 }{\sqrt{ 2 }} \times \frac{ \color{orangered}{\sqrt{ 2 }} }{ \color{orangered}{\sqrt{ 2 }}} }{ 1-\frac{1}{\sqrt{2}} } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{\frac{1\sqrt{2}}{2}}{1-\frac{1}{\sqrt{2}}} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\frac{\sqrt{2}}{2}}{1-\frac{1}{\sqrt{2}}}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 2 }}$. |
| ② | In denominator we have $ \sqrt{ 2 } \cdot \sqrt{ 2 } = 2 $. |
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