解：先化简分式，再将X^2-5X-1999=0代入。{(X-2)^3-(X-1)^2+1}/(X-2)={(X-2)^3-(X^2-2X+1)+1}/(X-2)= {(X-2)^3-(X^2-2X)}/(X-2)={(X-2)^3-X(X-2)}/(X-2)=(X-2){(X-2)^2-X}/(X-2)= (X-2)^2-X=X^2-5X+4= (X^2-5X-1999)+2003=2003
