Question

已知x为整数,且x+3分之2+3-x分之2+x2-9分之2x+18是整数,求符合条件的x

Answer 1

2/(x+3)+2/(3-x)+(2x+18)/(x^2-9)

=[2(x-3)-2(x+3)+(2x+18)]/(x^2-9)

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

=2/(x-3)为整数

所以,x-3=2,1,-1,-2

x=5,4,2,1