Найти сумму корней [latex] x^{2} +6+ \frac{2}{ x^{2} -9} =5x- \frac{4}{18-2 x^{2} } [/latex]

[latex]x^2 + 6 + \frac{2}{x^2-9} = 5x - \frac{4}{18-2x^2} [/latex] [latex] \frac{x^4 - 3x^2 - 52}{x^2-9} = \frac{5x^3 - 45x + 2}{x^2-9} [/latex] [latex]x^4 - 3x^2 - 52 = 5x^3 - 45x + 2[/latex] [latex]x^4 - 5x^3 - 3x^2 + 45x - 54 = 0[/latex] [latex](x-3)^2(x-2)(x+3) = 0 [/latex] [latex](x-3)^2 = 0 ; x - 2 = 0; x + 3 = 0[/latex] [latex]x = 3 ; x = 2 ; x = -3[/latex] [latex]x = 2[/latex]