\(\frac{2002x2001-1}{2000x2002+2001}=\frac{2002x\left(2000+1\right)-1}{2000x2002+2001}=\frac{2002x2000+2002-1}{2000x2002+2001}\)
\(=\frac{2002x2000+2001}{2000x2002+2001}=1\)
\(\frac{2002\times2001-1}{2000\times2002+2001}=\frac{2002\times\left(2001+1\right)-1}{2000\times2002+2001}\)
\(=\frac{2002\times2002-1}{2000\times2002+2001}\)
\(=\frac{2002\times2000+2001}{2000\times2002+2001}=1\)
\(\frac{2002x2001-1}{2000x2002+2001}\)
= \(\frac{2002x2000+2002-1}{2000x2002+2001}\)
= \(\frac{2002x2001+2001}{2000x2002+2001}\) = 1
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