\(\frac{2006\times125+1000}{126\times2006-1006}=\frac{2006\times125+1000}{\left(125+1\right)\times2006-1006}=\frac{2006\times125+1000}{2006\times125+2006\times1-1006}\)
\(=\frac{2006\times125+1000}{2006\times125+1000}=1\)
\(\frac{2006.125+1000}{126.2006-1006}=\frac{2006.125+1000}{\left(125+1\right).2006-1006}=\frac{2006.125+1000}{125.2006+1.2006-1006}=\frac{2006.125+1000}{125.2006+1000}=1\)
\(\frac{2006\times125+1000}{126\times2006-1006}=\frac{2006\times125+1000}{2006\times125+2006-1006}=\frac{2006\times125+1000}{2006\times125+1000}=1\)