(x^2-4x+4) / (x^2-4) ÷ (x^2-2x)/(x+2) - 1/x + 1
= (x-2)^2 / ((x+2)(x-2)} ÷ x(x-2)/(x+2) - 1/x + 1
= (x-2)^2 / ((x+2)(x-2)} * (x+2)/{ x(x-2)} - 1/x + 1
= 1/ x - 1/x +1
=1
∴当原式有意义时,代数式的值与x无关
∴聪聪说的有理
(x^2-4x+4) / (x^2-4) ÷ (x^2-2x)/(x+2) - 1/x + 1
= (x-2)^2 / ((x+2)(x-2)} ÷ x(x-2)/(x+2) - 1/x + 1
= (x-2)^2 / ((x+2)(x-2)} * (x+2)/{ x(x-2)} - 1/x + 1
= 1/ x - 1/x +1
=1
∴当原式有意义时,代数式的值与x无关
∴聪聪说的有理