OosakaNoOusama

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

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

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