已知a/b=3/5 求a/(a+b)+a/(a-b)-b²/(a²-b²)的值

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已知a/b=3/5 求a/(a+b)+a/(a-b)-b²/(a²-b²)的值

已知a/b=3/5 求a/(a+b)+a/(a-b)-b²/(a²-b²)的值

a/b=3/5,则设
a=3k b=5k
于是
a/(a+b)+a/(a-b)-b²/(a²-b²)
=3k/(3k+5K)+3k/(3k-5k)-25k²/(9k²-25k²)
=3k/(8K)+3k/(-2k)-25k²/(-16k²)
=3/8-3/2+25/16
=6/16-24/16+25/16
=7/16

a/(a+b)+a/(a-b)-b²/(a²-b²)
=a(a-b)/(a+b)(a-b) +a(a+b)/(a+b)(a-b) -b²/(a+b)(a-b)
=[a(a-b)+a(a+b)-b²]/(a+b)(a-b)
=(2a²-b²)/(a²-b²)
=[2(a/b)²-1]/[(a/b)²-1]
=[2×9/25-1)/(9/25-1)
=7/16

即b=3a/5
所以原式=a/(a+3a/5)+a/(a-3a/5)-(3a/5)²/[a²-(3a/5)²]
=5/8+5/2-9/16
=41/16