Question

已知X是整数且X+3分之2+3-X分之2+X的平方-9分之2X+18位整数,求所有符合条件的X的值的和

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).