先化简,再求值:a+2b/a+b+2b²/a²-b²,其中a=-2,b=3/1

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先化简,再求值:a+2b/a+b+2b²/a²-b²,其中a=-2,b=3/1
先化简,再求值:a+2b/a+b+2b²/a²-b²,其中a=-2,b=3/1

先化简,再求值:a+2b/a+b+2b²/a²-b²,其中a=-2,b=3/1
(a+2b)/(a+b)+2b²/(a²-b²)
=[(a+2b)(a-b)+2b²]/[(a+b)(a-b)]
=[a²+ab-2b²+2b²]/[(a+b)(a-b)]
=(a²+ab)/[(a+b)(a-b)]
=[a(a+b)]/[(a+b)(a-b)]
=a/(a-b)
=-2/(-2-1/3)
=-2/(-7/3)
=-2×(-3/7)
=6/7
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=(a+2b)(a-b)/(a+b)(a-b)+2b²/(a+b)(a-b)
=(a²+ab-2b²+2b²)/(a+b)(a-b)
=a(a+b)/(a+b)(a-b)
=a/(a-b)
当a=-2,b=1/3时
原式=-2/(-2-1/3)
=6/7