Question

решите уравнение
x+3//x^2-x-x-5//x+x^2=x-6//1-x^2
// деление

Answer 1

$frac{x+3}{x^2-x} - frac{x-5}{x+x^2} = frac{x-6}{1-x^2} \\ frac{x+3}{x(x-1)} - frac{x-5}{x(1+x)} = frac{x-6}{(1-x)(1+x)}; ,; ; ODZ:; xne 0; ,; xne 1; ,; xne -1\\frac{(x+3)(x+1)-(x-5)(x-1)}{x(x-1)(x+1)} = frac{x-6}{-(x-1)(x+1)} \\frac{x^2+4x+3-(x^2-6x+5)}{x(x-1)(x+1)}+ frac{x-6}{(x-1)(x+1)}=0\\ frac{10x-2+x(x-6)}{x(x-1)(x+1)} =0 \\ frac{x^2+4x-2}{x(x-1)(x+1)} =0\\x^2+4x-2=0; ,; ; ; D/4=4+2=6\\x_1= -8-sqrt8=-8-sqrt6 ; ; ;; ; ; x_2=-8+sqrt{6}$