Răspuns :
Notezi fractia cu F (x)
Pui conditia de existenta a logaritmului x>0
Inecuatia devine
(x-1)/lnx+2)>0
x-1=0 x=1
lnx+2=0 => lnx=-2 => x=e^(-2)=1/e^2
Faci tabelul de variatie
x lo.............1/e².......................1................................∞
_______________________________________
x-1 l- - - - - - - -- - - - - - 0+ + + + + + +
________________________________________
ln x+2 / - - - - 0+ + + + + + + + + + +
____________________________________________
f(x) l + + +l- - - - - - - 0+ + + + + + +
Deci x∈(O, 1/e²)U(1 ,+∞)
Pui conditia de existenta a logaritmului x>0
Inecuatia devine
(x-1)/lnx+2)>0
x-1=0 x=1
lnx+2=0 => lnx=-2 => x=e^(-2)=1/e^2
Faci tabelul de variatie
x lo.............1/e².......................1................................∞
_______________________________________
x-1 l- - - - - - - -- - - - - - 0+ + + + + + +
________________________________________
ln x+2 / - - - - 0+ + + + + + + + + + +
____________________________________________
f(x) l + + +l- - - - - - - 0+ + + + + + +
Deci x∈(O, 1/e²)U(1 ,+∞)