2/(x+3)+2/(3-x)+(2x+18)/(x^2-9)
=[2(x-3)-2(x+3)+(2x+18)]/(x^2-9)
=(2x+6)/(x^2-9)
=2/(x-3)为整数
所以,x-3=2,1,-1,-2
x=5,4,2,1