原式=[(x²-2x)/(x²-4)]÷[x-2-(2x-4)/(x+2)]
={x(x-2)/[(x+2)(x-2)]÷[(x-2)(x+2)/(x+2)-2(x-2)/(x+2)]
=[x/(x+2)]÷{[(x-2)(x+2)-2(x-2)]/(x+2)}
=[x/(x+2)]÷[(x-2)(x+2-2)/(x+2)]
=[x/(x+2)]÷[x(x-2)/(x+2)]
=[x/(x+2)]×{(x+2)/[x(x-2)]}
=1/(x-2)
=1/(2+√2-2)
=1/√2
=(√2)/2