先化简,再求值:(a2-2ab+b2)/(a2-b2)/(1/a-1/b),其中a=根号2+1,b=根号2-1

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先化简,再求值:(a2-2ab+b2)/(a2-b2)/(1/a-1/b),其中a=根号2+1,b=根号2-1

先化简,再求值:(a2-2ab+b2)/(a2-b2)/(1/a-1/b),其中a=根号2+1,b=根号2-1
先化简,再求值:(a2-2ab+b2)/(a2-b2)/(1/a-1/b),其中a=根号2+1,b=根号2-1

先化简,再求值:(a2-2ab+b2)/(a2-b2)/(1/a-1/b),其中a=根号2+1,b=根号2-1
原式=(a-b)²/(a+b)(a-b)÷(b-a)/ab
=(a-b)/(a+b)×[-ab/(a-b)]
=-ab/(a+b)
=-(2-1)/(2√2)
=-√2/4

:(a2-2ab+b2)/(a2-b2)/(1/a-1/b),
=(a-b)^2÷(a-b)(a+b)÷[(b-a)/(ab)]
=-ab/(a+b)

(a2-2ab+b2)/(a2-b2)/(1/a-1/b)
=(a-b)²/(a-b)(a+b) /[(b-a)/ab]
=(a-b)/(a+b) *ab/(b-a)
=-ab/(a+b)
=-1/(√2+1+√2-1)
=-1/2√2
=-√2/4