Question

Rezolvați în R ecuația x-3/x-5 + 1/x = x+5/x(x-5)

Answer 1

$\frac{x - 1}{x - 5} + \frac{1}{x } = \frac{x + 5}{x \times (x - 5)} = 0$
$\frac{x \times ( x - 3) + x - 5(x + 5)}{x \times (x - 5)} = 0$
$\frac{ x \times (x - 3) + x - 5 - x - 5 }{x \times (x - 5)} = 0$
$\frac{ x^{2} - 3x - 5 - 5}{x \times (x - 5)} = 0$
$\frac{x^{2} + 2x - 5x - 10}{x \times (x - 5)} = 0$
$\frac{x \times (x + 2) - 5(x + 2)}{x \times (x - 5)} = 0$
$\frac{(x + 2) \times (x - 5)}{x \times (x - 5)} = 0$
$\frac{x + 2}{x} = 0$
$x + 2 = 0$
$x = - 2$


Succes!!!