[latex] \frac{1}{(x-1) ^{2} } + \frac{3}{x-1} -10=0[/latex] Решите уравнение, я вас умоляю!

[latex] \frac{1}{(x-1)^2} + \frac{3}{x - 1} - 10 = 0 [/latex] [latex] \frac{-10x^3 + 53x^2-91x + 51}{(x-2)^2(x-1)} = 0[/latex] [latex]-10x^3 + 53x^2 - 91x + 51 = 0 -(2x - 3)(5x^2 - 19x + 17) = 0 2x - 3 = 0 ; 5x^2 - 19x + 17 = 0 [/latex] [latex]x = \frac{3}{2} ; x^2 - \frac{19x}{5} + 17 = 0 \ \textless \ =\ \textgreater \ x^2 - \frac{19x}{5} = - \frac{17}{5} [/latex] [latex]x = 1,5 ; x^2 - \frac{19x}{5} + \frac{361}{100} = \frac{21}{100} \ \textless \ =\ \textgreater \ (x - \frac{19}{10})^2 = \frac{21}{100} [/latex] [latex]x1 = 1,5 ; x2 = \frac{19}{10} + \frac{ \sqrt{21} }{10} ; x3 = \frac{19}{10} - \frac{ \sqrt{21} }{10} [/latex]