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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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
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
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
原式=[(a-2)/a(a+2)-(a-1)/(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)
=1/(2-1)
=1
:【(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-1)]/a(a+2)² ×(a+2)/(a-4)
=(a²-4-a²+a)/a(a+2)(a-4)
=1/a(a+2)
当a=√2-1时
原式=1/(√2-1)(√2+1)=1
【(a-2/a²+2a)-(a-1/a²+4a+4)】÷(a-4/a+2)
=【(a-2)/a(a+2)-(a-1)/(a+2)²】÷(a-4/a+2)
=(a-2)/a(a-4)-(a-1)/(a+2)(a-4)
=【(a-2)(a+2)-(a-1)a】÷a(a-4)(a+2)
=(a²-4-a²+a)÷a(a-4)(a+2)
=1/a(a+2)
再将a=√2-1代入即可。
原式=1/(√2-1)(√2+1)=1