Question

Rezolvați in R ecuația. Va rog ajutati-mă!

Answer 1

$\frac{1}{x} + \frac{x + 1}{x - 3} = \frac{12}{x(x - 3)}$

$\frac{x - 3}{x(x - 3)} + \frac{x(x + 1)}{x(x - 3)} = \frac{12}{x(x - 3)}$

$x - 3 + x(x + 1) = 12$

$x - 3 + {x}^{2} + x = 12$

${x}^{2} + x + x - 3 - 12 = 0$

${x}^{2} + 2x - 15 = 0$

${x}^{2} + 5x - 3x - 15 = 0$

$x(x + 5) - 3(x + 5) = 0$

$(x + 5)(x - 3) = 0$

$x + 5 = 0 = > x = - 5\:\in\:\mathbb{R}$

$x - 3 = 0 = > x = 3\:\in\:\mathbb{R}$