Answer:

Set ax? +bx？ + 1=(x？ -x- 1)(cx+d), i.e.

Axe? +bx？ + 1=(x？ -x- 1)(cx+d)=cx？ +(d-c)x？ -(c+d)x-d, so

C=a, d=- 1, c+d=0, b=d-c, then A = 1, B =-2, C = 1, D =- 1, that is, x? -2x？ + 1=(x？ -x- 1)(x- 1), so a= 1 and b=-2.

This kind of problem uses the method of undetermined coefficients, and then expands to find these coefficients, and the answer comes out