Question

6-x2/x-6x+x+6/x-6=3/x​

Answer 1

Răspuns:

$x=-8$

Explicație pas cu pas:

$\frac{6-x^2}{x^2-6x} +\frac{x+6}{x-6} =\frac{3}{x} \\\frac{6-x^2}{x(x-6)} +\frac{x(x+6)}{x(x-6)} =\frac{3(x-6)}{x(x-6)} \\6-x^2+x(x+6)=3(x-6)\\6-x^2+x^2+6x=3x-18\\6+6x=3x-18\\3x=-24\\x=-8$

Answer 2

Explicație pas cu pas:

$\dfrac{6 - {x}^{2} }{ {x}^{2} - 6x} + \dfrac{x + 6}{x - 6} = \dfrac{3}{x}$

$\dfrac{6 - {x}^{2} }{x(x - 6)} + \dfrac{^{x)} x + 6}{x - 6} = \dfrac{^{x - 6)}3}{x}$

x ≠ 0, x ≠ 6

$6 - {x}^{2} + x(x + 6) = 3(x - 6)$

$6 - {x}^{2} + {x}^{2} + 6x = 3x - 18$

$6x - 3x = - 18 - 6$

$3x = - 24 \implies x = - 8$