$ĐKXĐ:$ $x \neq 0; x \neq -2$

$Từ$ $PT (1):$ $\frac{144x}{x.(x +2)} - \frac{100.(x +2)}{x.(x +2)} = \frac{2x.(x +2)}{x.(x +2)}$

$⇒ 144x -100.(x +2) = 2x.(x +2)$

$⇔ 144x -100x -200 -2x² -4x = 0$

$⇔ -2x² +40x -200 = 0$

$⇔ -2.(x² -20x +100) = 0$

$⇔ -2.[x.(x -10) -10.(x -10)] = 0$

$⇔ -2.(x -10).(x -10) = 0$

$⇔ -2.(x -10)² = 0$

$⇔ x -10 = 0$

$⇔ x = 10$ $(T/m$ $đkxđ)$

$Vậy$ $S =$ {$10$}

Ta có: $\dfrac{144}{x+2} - \dfrac{100}{x} = 2 (ĐKXĐ: x \neq -2 ; x \neq 0)$

    ⇔  $\dfrac{144x}{x(x +2)}  - \dfrac{100(x+2)}{x(x+2)} = \dfrac{2x(x+2)}{x(x+2)}$

    ⇔  $\dfrac{144x - 100(x+2)}{x(x+2)} = \dfrac{2x^{2} + 4x}{x(x+2)}$
    ⇒   $144x - 100x - 200 = 2x^{2} + 4x$

    ⇔  $44x - 200 = 2x^{2} + 4x$

    ⇔  $2x^{2} + 4x - 44x + 200 = 0$
    ⇔  $2x^{2} - 40x + 200 = 0$

    ⇔  $2(x^{2} - 20x + 100) = 0$

    ⇔  $2(x - 10)^{2} = 0$

    ⇔  $(x - 10)^{2} = 0$

    ⇔  $x - 10 = 0$

    ⇔  $x = 10$ $\textrm{(Thỏa mãn ĐKXĐ)}$

Vậy phương trình có tập nghiệm là $S=$ {${10}$}