先化简,再求值;x的平方-4分之x的平方-2x除(x-2-(x+2分之2x-4)),其中x=2+根号2

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)
当x=2+√2时
原式=1/(2+√2 -2)
=1/√2
=(1×√2)/(√2×√2)
=(√2)/2