鸡蛋哥哥绘本故事图片:化简:b/(a+b) + b/(a -b) +(a^2+b^2)/(a^2 -b^2)

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b/(a+b) + b/(a -b) +(a^2+b^2)/(a^2 -b^2)
= b(a-b)/(a+b)(a-b) + b(a+b)/(a -b)(a+b) +(a^2+b^2)/(a^2 -b^2)
= (ab-b^2)/(a^2 -b^2 + (ab+b^2)/(a^2 -b^2) +(a^2+b^2)/(a^2 -b^2)
= (ab-b^2+ab+b^2+a^2+b^2)/(a^2 -b^2)
= (a^2+2ab+b^2)/(a^2 -b^2)
= (a+b)^2/(a+b)(a-b)
= (a+b)/(a-b)

=[b(a-b)+b(a+b)]/[a^2-b^2]+[a^2+b^2]/[a^2-b^2]
=[2ab+a^2+b^2]/[a+b][a-b]
=[a+b]^2/[a+b][a-b]
=[a+b]/[a-b]