解
【1】
x²-x+1
=(x²-2x+1)+x
=(x-1)²+x
=(x-1)²+(x-1)+1
即：x²-x+1=(x-1)²+(x-1)+1
∴(x²-x+1)/(x-1)=[(x-1)²+(x-1)+1]/(x-1)=(x-1)+1+[1/(x-1)]
即原方程左边=（x-1)+1+[1/(x-1)]
原方程可化为：
(x-1)+1+[1/(x-1)]=a+[1/(a-1)]
移项可得：
(x-1)+[1/(x-1)]=(a-1)+[1/(a-1)]
令x-1=y,a-1=c.上面方程可化为：
y+(1/y)=c+(1/c)
【2】
此时,方程：
(x-1)+[1/(x-1)]=(a-1)+[1/(a-1)]的解为：
x₁-1=a-1 x₂-1=1/(a-1)
即：x₁=a.x₂=a/(a-1)