Question

先化简，再求值（x-1/x-x-2/x+1）÷2x平方 –x/x平方 +2x+1，其中x满足x平方-x-1=0

Answer 1

（(x-1)/x-(x-2)/(x+1）)÷(2x平方 –x)/(x平方 +2x+1)
=(x²-1-x²+2x)/[x(x+1)]×(x+1)²/x(2x-1)
=(2x-1)(x+1)²/[x²(x+1)(2x-1)]
=(x+1)/x²
因为
x²-x-1=0
即
x²=x+1
所以
原式=x²/x²=1

Answer 2

x^2-x-1=0
x^2=x+1

[(x-1)/x-(x-2)/(x+1)]÷(2x^2-x)/(x^2 +2x+1)
=[(x-1)(x+1)/x(x+1)-x(x-2)/x(x+1)]÷(2x^2-x)/(x+1)^2
=[(x^2-1)-x(x-2)]/x(x+1)]÷(2x^2-x)/(x+1)^2
=[(x^2-1-x^2+2x]/x(x+1)]÷(2x^2-x)/(x+1)^2
=(2x-1)/x(x+1)*(x+1)^2/(2x^2-x)
=(2x-1)/x*(x+1)/(2x^2-x)
=(2x-1)/x*(x+1)/x(2x-1)
=1/x*(x+1)/x
=(x+1)/x^2
=x^2/x^2
=1

Answer 3

（(x-1)/x-(x-2)/(x+1）)÷(2x平方 –x)/(x平方 +2x+1)
=(x²-1-x²+2x)/[x(x+1)]×(x+1)²/x(2x-1)
=(2x-1)(x+1)²/[x²(x+1)(2x-1)]
=(x+1)/x²
因为
x²-x-1=0
即
x²=x+1
所以
原式=x²/x²=1

Answer 4

（x-1/x-x-2/x+1）÷2x平方 –x/x平方 +2x+1
=[(x-1)/x-(x-2)/(x+1)]÷2(x²-x)/(x²+2x+1)
=[(x²-3x+2-x²+2x)/x(x+1)]÷2x(x-1)/(x+1)²
=(-x+2)/x(x+1)×(x+1)²/2x(x-1)
=(-x+2)(x+1)/2x(x-1)
=(-x²+x-2)/2(x²-x)
=-(x²-x-1+3)/2(x²-x-1+1)
=-3/2