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