先化简再求值：(x-4/x2-1)÷(x2-3x-4/ x2+2x+1)+1/x-1.其中x=5

题目

先化简再求值：(x-4/x2-1)÷(x2-3x-4/ x2+2x+1)+1/x-1.其中x=5
(x-4/x的平方-1)÷(x的平方-3x-4/ x的平方+2x+1)+1/x-1.其中x=5

答案

[(x-4)/(x^2-1)]÷[(x^2-3x-4)/(x^2+2x+1)]+1/(x-1)=[(x-4)/(x-1)(x+1)]÷[(x+1)(x-4)/(x+1)^2]+1/(x-1)=[(x-4)/(x-1)(x+1)]*[(x+1)^2/(x+1)(x-4)]+1/(x-1)=1/(x-1)+1/(x-1)=2/(x-1)