已知x2+x-1=0，求x(1−21−x)÷(x+1)−x(x2−1)x2−2x+1的值．

Question

已知x²+x-1=0，求x(1−(2)/(1−x))÷(x+1)−(x(x2−1))/(x2−2x+1)的值．

Answer 1

x(1−(2)/(1−x))÷(x+1)−(x(x2−1))/(x2−2x+1)
=x[(1−x−2)/(1−x)•(1)/(x+1)−((x−1)(x+1))/((x−1)2)]
=x((1)/(x−1)−(x+1)/(x−1))
=(−x2)/(x−1)，
∵x²+x-1=0，
∴-x²=x-1，
∴原式=(−x2)/(x−1)=1．
故答案为1．