ОДЗ :
0" alt="\frac{x-2}{3-x}>0" align="absmiddle" class="latex-formula">
(x - 2)(x - 3) < 0
+ - +
____________₀_________₀__________
2 ///////////////// 3
x ∈ (2 ; 3)
(\frac{1}{2})^{-1}\\\\\frac{x-2}{3-x} >2\\\\\frac{x-2}{3-x}-2>0\\\\\frac{x-2-6+2x}{3-x}>0\\\\\frac{3x-8}{3-x}>0\\\\-3(x-\frac{8}{3})(x-3)>0\\\\(x-2\frac{2}{3} )(x-3)<0" alt="\frac{x-2}{3-x} >(\frac{1}{2})^{-1}\\\\\frac{x-2}{3-x} >2\\\\\frac{x-2}{3-x}-2>0\\\\\frac{x-2-6+2x}{3-x}>0\\\\\frac{3x-8}{3-x}>0\\\\-3(x-\frac{8}{3})(x-3)>0\\\\(x-2\frac{2}{3} )(x-3)<0" align="absmiddle" class="latex-formula">
+ - +
_________₀___________₀_____________
2 2/3 /////////////// 3
x ∈ (2 2/3 ; 3)
С учётом ОДЗ, ответ : x ∈ ( 2 2/3 ; 3)