先化简再求值(X-X/X-1)除以(1+1/X的平方-1),其中X=根号2-1

题目

先化简再求值(X-X/X-1)除以(1+1/X的平方-1),其中X=根号2-1

答案

原式=[X-X/(X-1)]/[1+1/(X²-1)]
=[X(X-1)-X]/[X-1+1/(X+1)] 分子分母都乘以(X-1)
=(X²-2X)(X+1)/[X²-1+1] 分子分母都乘以 (X+1)
=(X-2)(X+1)/X 分子分母都除以X
= (√2-3)√2/(√2-1) 代入X=√2-1
= (2-3√2)/(√2-1)
= (2-3√2)(√2+1)
=2√2+2-6-3√2
=-4-√2