$\frac{x -2}{x +2} - \frac{1}{x} = \frac{1}{x.(x +2)}$ $(ĐKXĐ:$ $x \neq -2; x \neq 0)$
$⇔ \frac{x.(x -2)}{x.(x +2)} - \frac{x +2}{x.(x +2)} = \frac{1}{x.(x +2)}$
$⇔ x.(x -2) -x -2 = 1$
$⇔ x² -2x -x -2 = 1$
$⇔ x² -3x -3 = 0$
$⇔ (x - \frac{3}{2})² - \frac{21}{4} = 0$
$⇔ (x - \frac{3}{2} - \frac{√21}{2}).(x - \frac{3}{2} + \frac{√21}{2}) = 0$
$⇔ \left[ \begin{array}{l}x- \frac{3}{2} - \frac{√21}{2}=0\\x- \frac{3}{2} + \frac{√21}{2}=0\end{array} \right. ⇔ \left[ \begin{array}{l}x=\frac{3+\sqrt{21}}{2}\\x=\frac{3-\sqrt{21}}{2}\end{array} \right.$
$Vậy$ $S =$ {$\frac{3+\sqrt{21}}{2}; \frac{3-\sqrt{21}}{2}$}
