原表达式有意义的条件是：x≠0且x^2-1≠0
即：x≠-1，0，1
原式=[(x^2-2x+1)/(x^2-1)+(1/x)]÷[(x^2+1)/(x+1)(x-1)]
=[(x-1)^2/(x+1)(x-1)+(1/x)]÷[(x^2+1)/(x+1)(x-1)]
=[(x-1)/(x+1)+(1/x)]÷[(x^2+1)/(x+1)(x-1)]
={[x(x-1)+(x+1)]/[x(x+1)]}÷[(x^2+1)/(x+1)(x-1)]
=[(x^2+1)/x(x+1)]*[(x+1)(x-1)/(x^2+1)]
=(x-1)/x

然后，任意取一个x≠-1，0，1的值，就可以得到原式的值了。
例如：
x=-1时，原式=2
x=2时，原式=1/2
……