已知x2+3x-1=0，求代数式1x−2•x2−4x+4x+1−x−1x+2的值．

Question

已知x²+3x-1=0，求代数式(1)/(x−2)•(x2−4x+4)/(x+1)−(x−1)/(x+2)的值．

Answer 1

原式=(1)/(x−2)•((x−2)2)/(x+1)-(x−1)/(x+2)
=(x−2)/(x+1)−(x−1)/(x+2)
=(x2−4−x2+1)/((x+1)(x+2))
=−(3)/((x+1)(x+2))
=−(3)/(x2+3x+2)，
∵x²+3x-1=0，
∴x²+3x=1，
∴原式=-(3)/(1+2)=-1．