Решите неравенство! lgx/x^2-2x>0

ОДЗ : x > 0

0\\\\1)\left \{ {{lgx>0} \atop {x^{2}-2x>0 }} \right. \\\\\left \{ {{x>1} \atop {x(x-2)>0}} \right." alt="\frac{lgx}{x^{2}-2x }>0\\\\1)\left \{ {{lgx>0} \atop {x^{2}-2x>0 }} \right. \\\\\left \{ {{x>1} \atop {x(x-2)>0}} \right." align="absmiddle" class="latex-formula">

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0 2

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x ∈ (2 ; + ∞)

$2)\left \{ {{lgx<0} \atop {x^{2}-2x<0 }} \right.\\\\\left \{ {{x<1} \atop {x(x-2)<0}} \right.$

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0 2

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x ∈ (0 ; 1)

Ответ : (0 ; 1) ∪ (2 , + ∞)