Question

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Answer 1

$\frac{x-2}{x}>-\frac{1}{x}.$

Область определения неравенства: $x\ne0.\ (*)$

$\frac{x-2}{x}>-\frac{1}{x},\\\\\frac{x-2}{x}+\frac{1}{x}>0,\\\\\frac{x-2+1}{x}>0,\\\\\frac{x-1}{x}>0,\\\\x>1,\ x<0$

Ответ: $x>1,\ x<0.$