化简求值【(x-2/x²+2x)-(x-1/x²+4x+4)】/(x-4/x+2)其中x²+2x-1=0

问题描述:

化简求值【(x-2/x²+2x)-(x-1/x²+4x+4)】/(x-4/x+2)其中x²+2x-1=0

【(x-2/x²+2x)-(x-1/x²+4x+4)】/(x-4/x+2)
=[(x-2)/x(x+2)-(x-1)/(x+2)²]/[(x-4)/(x+2)] 约去x+2
=[(x+2)/x-(x-1)/(x+2)]/(x-4)
=[(x+2)(x-2)-x(x-1)]/x(x+2)(x-4)
=(x-4)/x(x+2)(x-4)
=1/x(x+2)
=1/(x²+2x)
=1