(2001+2002x1999)/(2001x2002--2003)
=(2001+2002x1999)/(1999x2002+4004--2003)
=(2001+2002x1999)/(2001+2002x1999)
=1
2001+2002x1999/2001x2002--2003
=2001+(2001+1)x1999/2001x(2000+2)--2003
=2001+2001*1999+1999/2001*2000+1999
=2001*2000+1999/2001*2000+1999
=1