先化简,再求值:x的平方-2x+1分之x的立方-x乘以(x分之x-1),其中x=根号2-1

题目

先化简,再求值:x的平方-2x+1分之x的立方-x乘以(x分之x-1),其中x=根号2-1

答案

[(x^3-x)/(x^2-2x+1)]*(x-1)/x
=[x(x^2-1)/(x-1)^2]*(x-1)/x
=[x(x-1)(x+1)/(x-1)^2]*(x-1)/x
=x+1
=√2-1+1 ……（因为x=√2-1)
=√2