\(\)\(\frac{2003x4+1998+2001x2002}{2002+2002x503+504x2002}=\frac{2002x4+4+1998+2001x2002}{2002x\left(1+503+504\right)}=\frac{2002x4+2002+2001x2002}{2002x1008}\)\(\frac{2002x\left(4+1+2001\right)}{2002x1008}=\frac{2002x2006}{2002x1008}\)=\(\frac{2006}{1008}=\frac{1003}{504}\)