题目

已知x为整数,且2／（x＋3）＋2／（3－x）＋（2x＋18）/（x＾2－9）为整数,求所有符合条件x值的和．

提问时间：2020-10-31

答案

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