Question

Помогите с решением, пожалуйста

Answer 1

$\frac{x\, (x-5)}{\frac{2}{x-8}-\frac{1}{x-7}}=\frac{6}{\frac{1}{7-x}+\frac{2}{x-8}}\\\\ODZ:\; \; x\ne 8\; ;\; x\ne 7\; ;\; \; \frac{2}{x-8}\ne \frac{1}{x-7}\; \to \; x\ne 6\\\\\frac{x\, (x-5)}{\frac{2x-14-x+8}{(x-8)(x-7)}}-\frac{6}{\frac{x-8+14-2x}{(7-x)(x-8)}} =0\\\\\frac{x\, (x-5)(x-8)(x-7)}{x-6}-\frac{6(7-x)(x-8)}{-x+6}=0\\\\\frac{x\, (x-5)(x-8)(x-7)}{x-6}-\frac{6\, (x-7)(x-8)}{x-6}=0\\\\\frac{(x-8)(x-7)\cdot (x^2-5x-6)}{x-6}=0\; \; \Rightararow \\\\x^2-5x-6=0\; ,\; \; x\ne 6\; ,\; x\ne 8\; ,\; x\ne 7$

$D=5^2+4\cdot 6=49\\\\x_1=-1\; ,\; \; x_2=6\\\\x_1+x_2=-1+6=5\; -\; \; otvet.$