a) $\frac{{2006 \times 2005 - 1}}{{2004 \times 2006 + 2005}} = \frac{{2006 \times (2004 + 1) - 1}}{{2004 \times 2006 + 2005}}$ $ = \frac{{2006 \times 2004 + 2006 - 1}}{{2004 \times 2006 + 2005}}$ $ = \frac{{2006 \times 2004 + 2005}}{{2004 \times 2006 + 2005}} = 1$   b) $\frac{{1999 \times 2001 - 1}}{{1998 + 1999 \times 2000}} \times \frac{7}{5} = \frac{{1999 \times \left( {2000 + 1} \right) - 1}}{{1998 + 1999 \times 2000}} \times \frac{7}{5}$ $ = \frac{{1999 \times 2000 + 1999 - 1}}{{1998 + 1999 \times 2000}} \times \frac{7}{5}$ $ = \frac{{1999 \times 2000 + 1998}}{{1998 + 1999 \times 2000}} \times \frac{7}{5}$ $ = 1 \times \frac{7}{5} = \frac{7}{5}$   c) $\frac{{1313}}{{2121}} \times \frac{{165165}}{{143143}} \times \frac{{424242}}{{151515}} = \frac{{13}}{{21}} \times \frac{{165}}{{143}} \times \frac{{42}}{{15}}$ $ = \frac{{13}}{{21}} \times \frac{{15 \times 11}}{{13 \times 11}} \times \frac{{21 \times 2}}{{15}} = 2$   d) $\frac{{1995 \times 1993 - 18}}{{1975 + 1993 \times 1994}} = \frac{{\left( {1994 + 1} \right) \times 1993 - 18}}{{1975 + 1993 \times 1994}}$        $ = \frac{{1994 \times 1993 + 1993 - 18}}{{1975 + 1993 \times 1994}}$        $ = \frac{{1994 \times 1993 + 1975}}{{1975 + 1993 \times 1994}} = 1$