1/(x-1)+11/(x-11)=9/(x-9)+10/(x-10)

[latex] \frac{1}{x-1} + \frac{11}{x-11}= \frac{9}{x-9}+ \frac{10}{x-10}\\\\ \frac{x-11+11x-11}{(x-1)(x-11)}= \frac{9x-90+10x-90}{(x-9)(x-10)}\\\\ \frac{12x-22}{(x-1)(x-11)}= \frac{19x-180}{(x-9)(x-10)}\\\\ (12x-22)(x-9)(x-10)=(19x-180)(x-1)(x-11)\\\\ (12x^2-130x+198)(x-10)=(x^2-12x+11)(19x-180)\\\\ 12x^3-250x^2+1498x-1980=19x^3-408x^2+2369x-1980\\\\ -7x^3+158x^2-871x=0\\\\ -x(7x^2-158x+871)=0\\\\ -x=0\\ x=0\\\\ 7x^2-158x+871=0\\ D=24964-24388=576; \ \sqrt{D}=24\\\\ x_{1/2}= \frac{158\pm 24}{14}\\\\ x_1=\frac{182}{14}=13\\\\ x_2=\frac{134}{14}=\frac{67}{7}=9\frac{4}{7}[/latex] Ответ: [latex]x_1=0;x_2=9 \frac{4}{7}; x_3=13 [/latex]