把关于X的方程(x^2-X+1)/(X-1)=a+1/(a+1)变形为x+1/x=c+1/c的形式是()解是()
问题描述：
把关于X的方程(x^2-X+1)/(X-1)=a+1/(a+1)变形为x+1/x=c+1/c的形式是()解是()
答
(x^2-X+1)/(X-1)=[X(x-1)+1]/(X-1)=X+1/(X-1)
减1得
（X-1）+1/(X-1)=（a+1）+1/(a+1)
因为x+1/x=c+1/c的解是X=C或X=1/C
所以（X-1）+1/(X-1)=（a+1）+1/(a+1)的解是X-1=a+1或X-1=1/(a+1)
得X=a+2或X=1+1/(a+1)