已知x为整数,且[2/(x+3)]+[2/(3-x)]+[(2x+18)/(x2-9)]为整数,则所有符合条件的x值的和为多少?

已知x为整数,且[2/(x+3)]+[2/(3-x)]+[(2x+18)/(x2-9)]为整数,则所有符合条件的x值的和为多少?
已知x为整数,且[2/(x+3)]+[2/(3-x)]+[(2x+18)/(x2-9)]为整数,则所有符合条件的x值的和为多少?

已知x为整数,且[2/(x+3)]+[2/(3-x)]+[(2x+18)/(x2-9)]为整数,则所有符合条件的x值的和为多少?
2/(x+3)]+[2/(3-x)]+[(2x+18)/(x2-9)
=2(x+3+3-x)/(x+3)(3-x)+(2x+18)/(x+3)(x-3)
=[12-(2x+18)]/(x+3)(3-x)
=2(x+3)/(x+3)(x-3)
=2/(x-3)
=>(x-3)=+-1,+-2
x=4,2,5,1,
1+2+4+5=12