已知x为整数,且(x+3)分之2+(3-x)分之2+(x²-9)分之(2x+18)为整数,求x的值急_数学解答

已知x为整数,且(x+3)分之2+(3-x)分之2+(x²-9)分之(2x+18)为整数,求x的值
急

人气：191 ℃　时间：2020-03-29 02:48:05

解答

2/(x+3)+2/(3-x)+(2x+18)/(x^2-9)
=2/(x+3)-2/(x-3)+(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).
因此,x - 3 必然是2的因数,2有4个因数,1,-1,2,-2,
所以x=5,1,4,2