Question

решить уравнение, найти НОЗ и ОДЗ​

Answer 1

$\frac{x-4}{x}-\frac{2x-5}{x-6}=0\; ,\; \; \; ODZ:\; x\ne 0\; ,\; x\ne 6\\\\\frac{(x-4)(x-6)-x(2x-5)}{x(x-6)}=0\\\\\frac{x^2-10x+24-2x^2+5x}{x(x6)}=0\\\\\frac{-x^2-5x+24}{x(x-6)}=0\\\\\frac{-(x^2+5x-24)}{x(x-6)}=0\; \; \to \; \; x^2+5x-24=0\; ,\; x_1=3\; ,\; x_2=-8\; \; (teorema\; Vieta)\\\\\frac{-(x-3)(x+8)}{x(x-6)}=0\\\\Onvet:\; \; x_1=3\; ,\; x_2=-8\; .$