Giải thích các bước giải:
1. \(\begin{array}{l}
A = ({x^2} + x + 1 + x).({x^2} - x + 1 - x).\frac{{(x - \sqrt 2 )(x + \sqrt 2 )}}{{x{{(1 + x)}^2}{{(1 - x)}^2}}}\\
A = {(x + 1)^2}{(x - 1)^2}.\frac{{(x - \sqrt 2 )(x + \sqrt 2 )}}{{x{{(1 + x)}^2}{{(1 - x)}^2}}}\\
A = \frac{{(\sqrt 2 - x)(x + \sqrt 2 )}}{x}
\end{array}\)
2. Khi \(x = \sqrt {6 + 2\sqrt 2 } \):
\(A = \frac{{(\sqrt 2 - x)(x + \sqrt 2 )}}{x} = \frac{{(\sqrt 2 - \sqrt {6 + 2\sqrt 2 } )(\sqrt {6 + 2\sqrt 2 } + \sqrt 2 )}}{{\sqrt {6 + 2\sqrt 2 } }} = \frac{{ - 4 - 2\sqrt 2 }}{{\sqrt {6 + 2\sqrt 2 } }}\)
3. Để A=3:
\(\begin{array}{l}
A = \frac{{(\sqrt 2 - x)(x + \sqrt 2 )}}{x} = \frac{{2 - {x^2}}}{x} = 3\\
\Leftrightarrow {x^2} + 3x - 2 = 0\\
\Leftrightarrow x = \frac{{ - 3 + \sqrt {17} }}{2};x = \frac{{ - 3 - \sqrt {17} }}{2}
\end{array}\)
