Bài tập 5.18 trang 202 SBT Toán 11

\(\begin{array}{l}
f\left( x \right) = \left[ {\frac{{x - 1}}{{2(\sqrt x  + 1)}} + 1} \right].\frac{2}{{\sqrt x  + 1}}:{\left( {\frac{{\sqrt {x - 2} }}{{\sqrt {x + 2}  + \sqrt {x - 2} }} + \frac{{x - 2}}{{\sqrt {{x^2} - 4}  - x + 2}}} \right)^2}\\
 = \frac{{x + 2\sqrt x  + 1}}{{2\left( {\sqrt x  + 1} \right)}}.\frac{2}{{\sqrt x  + 1}}:{\left[ {\frac{{\sqrt {x - 2} }}{{\sqrt {x + 2}  + \sqrt {x - 2} }} + \frac{{\sqrt {x - 2} }}{{\sqrt {x + 2}  - \sqrt {x - 2} }}} \right]^2}\\
 = 1:{\left( {\frac{{\sqrt {x - 2} }}{{\sqrt {x + 2}  + \sqrt {x - 2} }} + \frac{{\sqrt {x - 2} }}{{\sqrt {x + 2}  - \sqrt {x - 2} }}} \right)^2}\\
 = 1:{\left[ {\frac{{\sqrt {{x^2} - 4}  - \left( {x - 2} \right) + \left( {x - 2} \right) + \sqrt {{x^2} - 4} }}{4}} \right]^2}\\
 = 1:{\left( {\frac{{\sqrt {{x^2} - 4} }}{2}} \right)^2} = \frac{4}{{{x^2} - 4}}
\end{array}\)

-- Mod Toán 11 HỌC247