原式 = ( 2 * 2002^2 )/( (1000^2 - 4) + (1003^2 - 1) )
= ( 2 * 2002^2 )/( (1000+2) (1000-2) + (1003 + 1)(1003 - 1) )
= ( 2 * 2002^2 )/( 1002*998 + 1004*1002 )
= ( 2 * 2002^2 )/ 1002 (1004+998)
= ( 2 * 2002^2 )/ 1002 *2002
= 2 / 1002
= 1/ 501
原式 = ( 2 * 2002^2 )/( (1000^2 - 4) + (1003^2 - 1) )
= ( 2 * 2002^2 )/( 1002*998 + 1004*1002 )
= ( 2 * 2002^2 )/ 1002 (1004+998)
= ( 2 * 2002^2 )/ 1002 *2002
= 2 *2002/ 1002
= 2002/ 501