先化簡在求值.(X^2+2X分之X-2-X^2+4X+4分之X-1)除X+2分之X-4.其中X^2+2X… 先化簡在求值.(X^2+2X分之X-2-X^2+4X+4分之X-1)除X+2分之X-4.其中X^2+2X-1=0.

先化簡在求值.(X^2+2X分之X-2-X^2+4X+4分之X-1)除X+2分之X-4.其中X^2+2X… 先化簡在求值.(X^2+2X分之X-2-X^2+4X+4分之X-1)除X+2分之X-4.其中X^2+2X-1=0.

原式={[(x-2)/(x²;+2x)]-[(x-1)/(x²;+4x+4)]}÷[(x-4)/(x+2)]
={(x-2)/[x(x+2)]-[(x-1)/(x+2)²;]}×[(x+2)/(x-4)]
=(x-2)/[x(x+2)]×[(x+2)/(x-4)]-[(x-1)/(x+2)²;]×[(x+2)/(x-4)]
=(x-2)/[x(x-4)]-(x-1)/[(x+2)(x-4)]
=[(x-2)(x+2)]/[x(x+2)(x-4)]-[x(x-1)]/[x(x+2)(x-4)]
=[(x-2)(x+2)-x(x-1)]/[x(x+2)(x-4)]
=(x²;-4-x²;+x)/[x(x+2)(x-4)]
=(x-4)/[x(x+2)(x-4)]
=1/[x(x+2)
=1/(x²;+2x)
因為x²;+2x-1=0
所以x²;+2x=1
所以
原式=1/1=1