Question

[(x-1)/x-(x-2)/(x+1)÷(2x2-x)/x2+2x+1) x2-x-1=0 先化简再求值

Answer 1

[(x-1)/x-(x-2)/(x+1)]÷[(2x²-x)/(x²+2x+1)]
=[(x²-1-x²+2x)/x(x+1)]÷[x(2x-1)/(x+1)²]
=[(2x-1)/x(x+1)]×[(x+1)²/x(2x-1)]
=(x+1)/x²
∵x²-x-1=0
∴x²=x+1
∴原式=(x+1)/x²=(x+1)/(x+1)=1

Answer 2

∵x²-x-1=0 ∴x²=x+1
∴[(x-1)/x-(x-2)/(x+1)÷(2x²-x)/(x²+2x+1)
={[(x-1)(x+1)-x(x-2)]/[x(x+1)] }×(x+1)²/[x(2x-1)]
=(2x-1)/[x(x+1)]×(x+1)²/[x(2x-1)]
=(x+1)/x²
=1