Question

已知x是整数,且1/(x+3)+1/(x-3)+6/(x^2-9)的值为整数,则所有符合条件的x的值的和为

Answer 1

1/(x+3)+1/(x-3)+6/(x^2-9)

=[(x-3)+(x+3)+6]/(x^2-9)

=(2x+6)/(x^2-9)

=2(x+3)/[(x+3)(x-3)]

=2/(x-3)

要式子为整数,则整数x只能为：1,2,4,5

1+2+4+5=12