User:OosakaNoOusama

舉例： Example: $$\frac{2+\sqrt{2}}{\sqrt{2}+1}$$

一些人認為： Some people think: $$\begin{align} \frac{2+\sqrt{2}}{\sqrt{2}+1} & = \frac{2+\cancel{\sqrt{2}}}{\cancel{\sqrt{2}}+1} \\ & = \frac{2}{\cancel{1}} \\ & = 2 \\ \end{align}$$

正確答案： Correct answer: $$\begin{align} \frac{2+\sqrt{2}}{\sqrt{2}+1} & = \frac{\sqrt{2}\left (\sqrt{2}+1\right )}{\sqrt{2}+1} \\ & = \frac{\sqrt{2}\cancel{\left (\sqrt{2}+1\right )}}{\cancel{\sqrt{2}+1}} \\ & = \sqrt{2} \\ \end{align}$$