Ta có:[tex]\frac{x+1}{x^2}=\frac{1}{x}+\frac{1}{x^2}=(\frac{1}{x^2}+2.\frac{1}{2}.\frac{1}{x}+\frac{1}{4})-\frac{1}{4}[/tex]
[tex]=(\frac{1}{x}+\frac{1}{2})^2-\frac{1}{4}\geq \frac{-1}{4}[/tex]
Dấu "=" xảy ra khi [tex]x=-2[/tex]
Vậy ...............................................................................................................................................................................