Đáp án:
b) \(\dfrac{{x + 2008}}{x}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)DK:x \ne \left\{ { - 1;0;1} \right\}\\
b)A = \left( {\dfrac{{x + 1}}{{x - 1}} - \dfrac{{x - 1}}{{x + 1}} - \dfrac{{{x^2} - 4x - 1}}{{1 - {x^2}}}} \right).\dfrac{{x + 2008}}{x}\\
= \left[ {\dfrac{{{{\left( {x + 1} \right)}^2} - {{\left( {x - 1} \right)}^2} + {x^2} - 4x - 1}}{{\left( {x - 1} \right)\left( {x + 1} \right)}}} \right].\dfrac{{x + 2008}}{x}\\
= \dfrac{{{x^2} + 2x + 1 - {x^2} + 2x - 1 + {x^2} - 4x - 1}}{{\left( {x - 1} \right)\left( {x + 1} \right)}}.\dfrac{{x + 2008}}{x}\\
= \dfrac{{{x^2} - 1}}{{\left( {x - 1} \right)\left( {x + 1} \right)}}.\dfrac{{x + 2008}}{x}\\
= \dfrac{{x + 2008}}{x}\\
c)A = \dfrac{{x + 2008}}{x} = 1 + \dfrac{{2008}}{x}\\
A \in Z\\
\Leftrightarrow \dfrac{{2008}}{x} \in Z\\
\Leftrightarrow x \in U\left( {2008} \right)\\
\to \left[ \begin{array}{l}
x = 2008\\
x = - 2008\\
x = 1004\\
x = - 1004\\
x = 502\\
x = - 502\\
x = 251\\
x = - 251\\
x = 1\left( l \right)\\
x = - 1\left( l \right)
\end{array} \right.
\end{array}\)
