ASRJC Inequalities Tutorial Q1

Solve algebraically the inequality \(\frac{{{e}^{x}}\left( x+1 \right)}{x{{\left( x-2 \right)}^{2}}}\le 0\) .

Hence, solve \(\frac{1-\ln x}{\left( -x\ln x \right){{\left( \ln x+2 \right)}^{2}}}\le 0\) exactly.