Question

先化简再求值:(x-1分之x的平方-x+1)÷ 1-x分之4x的平方-4x+1,其中x满足x的平方+x-2=0

Answer 1

[(x²-x+1)/(x-1)]÷[(4x²-4x+1)/(1-x)]

=-[(x²-x+1)/(x-1)]*(x-1)/(2x-1)²

=-(x²-x+1)/(2x-1)²

∵x²+x-2=0 ∴x1=1 x2=-2

∴原式=-(1-1+1)/(2-1)²=-1或原式=-（4+2+1）/（-4-1）²=-7/25.