^解:
(1-1/x²)^(-1)+(1/x-x)^(-1)
=[(x²-1)/x²]^(-1)+[(1-x²)/x]^(-1)
=x²/(x²-1)+x/(1-x²)
=(x²-x)/(x²-1)
=(x-1)x/[(x+1)(x-1)]
=x/(x+1)
当x=√3-2时,
原式=x/(x+1)
=(√3-2)/(√3-2+1)
=(√3-2)(√3+1)/2
=(3+√3-2√3-2)/2
=(1-√3)/2
担心你手机显示不了平方符号,图片格式如下: