Đáp án:
$\begin{array}{l}
a)\left| x \right| \ge 0\forall x\\
\Rightarrow \left| x \right| + 1997 \ge 1997\forall x\\
\Rightarrow \dfrac{1}{{\left| x \right| + 1997}} \le \dfrac{1}{{1997}}\\
\Rightarrow \dfrac{{1996}}{{\left| x \right| + 1997}} \le \dfrac{{1996}}{{1997}}\\
\Rightarrow GTLN = \dfrac{{1996}}{{1997}}\,khi:x = 0\\
b)\left| x \right| \ge 0\\
\Rightarrow \left| x \right| + 1996 \ge 1996\\
\Rightarrow \dfrac{{\left| x \right| + 1996}}{{1997}} \ge \dfrac{{1996}}{{1997}}\\
\Rightarrow \dfrac{{\left| x \right| + 1996}}{{ - 1997}} \le \dfrac{{ - 1996}}{{1997}}\\
\Rightarrow GTLN = - \dfrac{{1996}}{{1997}}\,khi:x = 0
\end{array}$
