Với [tex]a\geq b\Rightarrow \frac{a}{b}-\frac{a+2001}{b+2001}=\frac{2001(a-b)}{b^2+2001b}\geq 0\Rightarrow \frac{a}{b}\geq \frac{a+2001}{b+2001}[/tex]
Với [tex]a< b\Rightarrow \frac{a}{b}-\frac{a+2001}{b+2001}=\frac{2001(a-b)}{b^2+2001b}< 0\Rightarrow \frac{a}{b}< \frac{a+2001}{b+2001}[/tex]