Bonjour,
1)
[tex] \dfrac{x^2-9}{3x} = 0; \quad x\neq 0 \\\\
x^2 - 9 = 0\\
x^2 = 9\\
x = \pm \sqrt9\\ x = \pm 3\\\\\boxed{S = \left\{-3; 3\right\}}[/tex]
2)
[tex]\dfrac{1}{x+1} - \dfrac{2}{x-1} = 0; \quad x \neq -1; x \neq 1\\\\\\
\dfrac{1\times(x-1)}{(x-1)\times(x+1)} - \dfrac{2\times (x+1)}{(x+1)\times(x-1)} = 0\\\\\\ \dfrac{(x-1)-2\times (x+1)}{(x+1)\times(x-1)} = 0\\\\\\ \dfrac{x-1-2x-2}{(x+1)\times(x-1)} = 0\\\\\\ \dfrac{-x-3}{(x+1)\times(x-1)} = 0\\\\
-x-3 = 0\\
-x = 3\\
x = -3\\\\
\boxed{S = \left\{3\right\}}[/tex]
3)
[tex] \dfrac{9x^2-25}{(x+2)(3x+5)} = 0; \quad x \neq -2, x\neq -\dfrac{5}{3}\\\\
9x^2 - 25 = 0\\
9x^2 = 25\\\\
x^2 = \dfrac{25}{9}\\\\
x = \pm \sqrt{ \dfrac{25}{9}} \\\\
x = \pm \dfrac{\sqrt{25}}{\sqrt{9}}\\\\
x = \pm \dfrac{5}{3}\\\\
\text{Comme } -\dfrac{5}{3} = \text{valeur interdite}\\\\
\boxed{S = \left\{\dfrac{5}{3}\right\}}[/tex]
