$\frac{2004 × 2007 + 6}{2005 × 2005 + 2009}$
= $\frac{(2005 - 1) × 2007 + 6}{2005 × 2005 + 2009}$
= $\frac{2005 × 2007 - 2007 + 6}{2005 × 2005 + 2009}$
= $\frac{2005 × (2005 + 2) - 2007 + 6}{2005 × 2005 + 2009}$
= $\frac{2005 × 2005 + 2005 × 2 - 2007 + 6}{2005 × 2005 + 2009}$
= $\frac{2005 × 2005 + 4010 - 2007 + 6}{2005 × 2005 + 2009}$
= $\frac{2005 × 2005 + 2009}{2005 × 2005 + 2009}$
Vậy $\frac{2004 × 2007 + 6}{2005 × 2005 + 2009}$ = $\frac{2005 × 2005 + 2009}{2005 × 2005 + 2009}$ = 1
