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