$\frac{3x -1}{x -1} - \frac{2x +5}{x -3} = 1$ $(ĐKXĐ:$ $x \neq 1; x \neq 3)$
$⇔ \frac{(x -3).(3x -1)}{(x -3).(x -1)} - \frac{(x -1).(2x +5)}{(x -1).(x -3)} = \frac{(x -1).(x -3)}{(x -1).(x -3)}$
$⇒ (x -3).(3x -1) - (x -1).(2x +5) = (x -1).(x -3)$
$⇔ 3x² -10x +3 -2x² -3x +5 = x² -4x +3$
$⇔ x² -13x +8 = x² -4x +3$
$⇔ x² -x² -13x +4x = 3 -8$
$⇔ -9x = -5$
$⇔ x = \frac{5}{9}$ $(T/m$ $đkxđ)$
$Vậy$ $S =$ {$\frac{5}{9}$}
