Question

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

Answer 1

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