\(\frac{2006\cdot125+1000}{126\cdot2006-1006}=\frac{2006\cdot\left(126-1\right)+1000}{126\cdot2006-1006}\)
\(=\frac{2006\cdot126-2006+1000}{126\cdot2006-1006}\)
\(=\frac{2006\cdot126-1006}{126\cdot2006-1006}\)
\(=1\)
\(\frac{2006x125+1000}{126x2006-1006}\)
\(=\frac{2006x125+1000}{\left(125+1\right)x2006-1006}\)
\(=\frac{2006x125+1000}{125x2006+1x2006-1006}\)
\(=\frac{2006x125+1000}{125x2006+2006-1006}\)
\(=\frac{2006x125+1000}{125x2006+1000}\)
\(=1\)