若a=1/(2+更号3),求(1-2a+a的平方)/(a-1)再-更号(a的平方-2a+1)/(a的平方-a)的值.
要有解答过程
参考答案:因为(2+√3)(2-√3)=1,所以a=2-√3,a-1=1-√3<0,
[(1-2a+a²)/(a-1)]-[√(a²-2a+1)/(a²-a)]
=[(a-1)²/(a-1)]-|a-1|/[a(a-1)]
=(a-1)-(1-a)/[a(a-1)]
=a-1+(1/a)
=2-√3-1+2+√3
=3
要有解答过程
参考答案:因为(2+√3)(2-√3)=1,所以a=2-√3,a-1=1-√3<0,
[(1-2a+a²)/(a-1)]-[√(a²-2a+1)/(a²-a)]
=[(a-1)²/(a-1)]-|a-1|/[a(a-1)]
=(a-1)-(1-a)/[a(a-1)]
=a-1+(1/a)
=2-√3-1+2+√3
=3