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先化简,再求值(3a/a-1 - a/a+1)*a^2-1/a,其中a=根号2-2
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先化简,再求值(3a/a-1 - a/a+1)*a^2-1/a,其中a=根号2-2
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答案和解析
[3a/(a-1) - a/(a+1)]*(a^2-1)/a
=a[3/(a-1) - 1/(a+1)]*(a^2-1)/a
=[3/(a-1) - 1/(a+1)]*(a^2-1)
=[3(a+1)-(a-1)]/[(a-1)(a+1)]*(a^2-1)
=[3a+3-a+1]/(a^2-1)*(a^2-1)
=3a+3-a+1
=3a-a+1+3
=2a+4
=2(√2-2)+4
=2√2-4+4
=2√2
=a[3/(a-1) - 1/(a+1)]*(a^2-1)/a
=[3/(a-1) - 1/(a+1)]*(a^2-1)
=[3(a+1)-(a-1)]/[(a-1)(a+1)]*(a^2-1)
=[3a+3-a+1]/(a^2-1)*(a^2-1)
=3a+3-a+1
=3a-a+1+3
=2a+4
=2(√2-2)+4
=2√2-4+4
=2√2
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