Question

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

Answer 1

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

Ответ: $x_1=0;x_2=9 frac{4}{7}; x_3=13$