求使分式(9x^2-18x+9)/(x-1)^3的值为整数的x的值

题目

求使分式(9x^2-18x+9)/(x-1)^3的值为整数的x的值

答案

答
(9x^2-18x+9)/(x-1)^3
=9(x^2-2x+1)/(x-1)^3
=9(x-1)^2/(x-1)^3
=9/(x-1)
值为整数
x-1被9整除
∴x-1=1,3,9,-1,-3,-9
∴x=2,4,10,0,-2,-8