Đáp án:
$\begin{array}{l}
A = \dfrac{{2{x^2} - 1}}{{{x^2} + 3}} = \dfrac{{2.\left( {{x^2} + 3} \right) - 2.3 - 1}}{{{x^2} + 3}}\\
= \dfrac{{2\left( {{x^2} + 3} \right)}}{{{x^2} + 3}} - \dfrac{7}{{{x^2} + 3}}\\
= 2 - \dfrac{7}{{{x^2} + 3}}\\
Do:{x^2} \ge 0\\
\Leftrightarrow {x^2} + 3 \ge 3\\
\Leftrightarrow \dfrac{1}{{{x^2} + 3}} \le \dfrac{1}{3}\\
\Leftrightarrow \dfrac{7}{{{x^2} + 3}} \le \dfrac{7}{3}\\
\Leftrightarrow - \dfrac{7}{{{x^2} + 3}} \ge \dfrac{{ - 7}}{3}\\
\Leftrightarrow 2 - \dfrac{7}{{{x^2} + 3}} \ge 2 - \dfrac{7}{3}\\
\Leftrightarrow \dfrac{{2{x^2} - 1}}{{{x^2} + 3}} \ge \dfrac{{ - 1}}{3}\\
\Leftrightarrow GTNN:\dfrac{{2{x^2} - 1}}{{{x^2} + 3}} = - \dfrac{1}{3}\\
Khi:x = 0
\end{array}$
Vậy GTNN của biểu thức bằng $ - \dfrac{1}{3}$ khi x=0
