[latex]frac{2}{ x^{2} +x}- frac{1}{ x^{2} } = frac{1}{6x}[/latex] [latex]frac{2}{x(x+1)}- frac{1}{ x^{2} }=frac{1}{6x}[/latex] Dziedzina : [latex]x eq -1,x eq 0[/latex] [latex]frac{2}{x(x+1)}- frac{1}{ x^{2} }-frac{1}{6x}=0[/latex] [latex]frac{12x}{6x^2(x+1)}- frac{6(x+1)}{6 x^{2}(x+1) }-frac{x(x+1)}{6 x^{2}(x+1) }=0[/latex] [latex]frac{12x- 6x-6-x^2-x}{6 x^{2}(x+1) }=0[/latex] [latex]frac{- x^2 + 5x - 6}{6 x^{2}(x+1) }=0[/latex] [latex]- x^2 + 5x - 6=0 /:(-1)[/latex] [latex]x^2-5x+6=0[/latex] [latex]Delta=(-5)^2-4cdot 1cdot 6=25-24=1[/latex] [latex] sqrt{Delta}= sqrt{1}=1[/latex] [latex]x_1= frac{5-1}{2}=2[/latex] [latex]x_2= frac{5+1}{2}=3[/latex]
[latex]frac{2}{ x^{2} +x}-frac{1}{ x^{2} } = frac{1}{6x}\\frac{2}{x(x+1)} -frac{1}{ x^{2} } - frac{1}{6x} = 0\\Z:\x eq 0\x+1 eq 0\x eq -1\\D = R-lbrace-1;0 brace\\frac{12x-6(x+1)-x(x+1)}{6 x^{2} (x+1)} = 0\\12x-6x-6- x^{2} -x = 0\\- x^{2} +5x-6 = 0 |*(-1)\\ x^{2} -5x+6 = 0\\Delta = 25-24 = 1\\sqrt{Delta} = 1\\x_1 = frac{5-1}{2} = 2\\x_2 = frac{5+1}{2} = 3[/latex]
