\(\begin{array}{l}
\dfrac{{2005 \times 2006 - 1}}{{2006 \times 2004 + 2005}} = \dfrac{{\left( {2004 + 1} \right) \times 2006 - 1}}{{2006 \times 2004 + 2005}}\\
= \dfrac{{2004 \times 2006 + 2006 \times 1 - 1}}{{2006 \times 2004 + 2005}} = \dfrac{{2004 \times 2006 + 2005}}{{2006 \times 2004 + 2005}} = 1
\end{array}\)