已知(2x^3-5x^2-x+1)/(x^2-bx+1)=ax+1,则a+b=
问题描述：
已知(2x^3-5x^2-x+1)/(x^2-bx+1)=ax+1,则a+b=
答
(2x^3-5x^2-x+1)/(x^2-bx+1)=ax+1(2x^3-5x^2-x+1)=(x^2-bx+1)(ax+1)(x^2-bx+1)(ax+1)=(x^2-bx+1)*ax+(x^2-bx+1)=ax^3-abx^2+ax+(x^2-bx+1)=ax^3-(ab-1)x^2+(a-b)x+1a=2,ab-1=5,a-b=-1所以a=2,b=3a+b=5