[tex] \frac{1}{x} + \frac{x + 1}{x - 3} = \frac{12}{x(x - 3)} [/tex]
[tex] \frac{x - 3}{x(x - 3)} + \frac{x(x + 1)}{x(x - 3)} = \frac{12}{x(x - 3)} [/tex]
[tex]x - 3 + x(x + 1) = 12[/tex]
[tex]x - 3 + {x}^{2} + x = 12[/tex]
[tex] {x}^{2} + x + x - 3 - 12 = 0[/tex]
[tex] {x}^{2} + 2x - 15 = 0[/tex]
[tex] {x}^{2} + 5x - 3x - 15 = 0[/tex]
[tex]x(x + 5) - 3(x + 5) = 0[/tex]
[tex](x + 5)(x - 3) = 0[/tex]
[tex]x + 5 = 0 = > x = - 5\:\in\:\mathbb{R}[/tex]
[tex]x - 3 = 0 = > x = 3\:\in\:\mathbb{R}[/tex]
