{[(2A-2B)/(a^2-2AB+B^2)]+B/(A^2-B^2)}÷(3b+2a)/(a+b)

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{[(2A-2B)/(a^2-2AB+B^2)]+B/(A^2-B^2)}÷(3b+2a)/(a+b)

{[(2A-2B)/(a^2-2AB+B^2)]+B/(A^2-B^2)}÷(3b+2a)/(a+b)
{[(2A-2B)/(a^2-2AB+B^2)]+B/(A^2-B^2)}÷(3b+2a)/(a+b)

{[(2A-2B)/(a^2-2AB+B^2)]+B/(A^2-B^2)}÷(3b+2a)/(a+b)
原式
=[2(a-b)/(a-b)²+b/(a+b)(a-b)]×(a+b)/(2a+3b)
=[2/(a-b)+b/(a+b)(a-b)]×(a+b)/(2a+3b)
=[2(a+b)+b]/(a+b)(a-b) ×(a+b)/(2a+3b)
=(2a+3b)/(a-b) ×1/(2a+3b)
=1/(a-b)