先化简,再求值:(x^2-4)/(x^2-4x+4)÷(x+2)/(x+1)-x/(x-2),其中x=2-根号2

问题描述:

先化简,再求值:(x^2-4)/(x^2-4x+4)÷(x+2)/(x+1)-x/(x-2),其中x=2-根号2

原式=(X+2)(X-2)/(X-2)²÷(X+2)/(X+1)-X/(X-2)
=(X+2)/(X-2)×(X+1)/(X+2)-X/(X-2)
=(X+1)/(X-2)-X/(X-2)
=1/(X-2)
代入X=2-√2
1/(-√2)=-√2/2