Question

ДАЮ 10 БАЛЛОВ!!!
Розв'яжіть рівняння: прикріпив фото.​

Answer 1

$\displaystyle\bf\\\frac{3x-1}{x} -\frac{4}{x-2} =\frac{10-9x}{x^{2} -2x} \\\\\\\frac{3x-1}{x} -\frac{4}{x-2} -\frac{10-9x}{x(x -2)} =0\\\\\\\frac{(3x-1)\cdot(x-2)-4x-10+9x}{x(x-2)} =0\\\\\\\frac{3x^{2} -6x-x+2+5x-10}{x(x-2)}=0\\\\\\\frac{3x^{2} -2x-8}{x(x-2)} =0\\\\\\\left \{ {{3x^{2} -2x-8=0} \atop {x\neq 0 \ , \ x\neq 2}} \right. \\\\\\3x^{2} -2x-8=0\\\\D=(-2)^{2} -4\cdot 3\cdot(-8)=4+96=100=10^{2} \\\\\\x_{1} =\frac{2-10}{6} =\frac{-8}{6} =-1\frac{1}{3}$

$\displaystyle\bf\\x_{2} =\frac{2+10}{6} =\frac{12}{6} =2-neyd\\\\\\Otvet: \ -1\frac{1}{3}$