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

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

(a^2-2ab)/(-ab+b^2)÷[a^2/(a-b)÷(2ab)/(2b-a)]
=a(a-2b)/[-b(a-b)] ×(a-b)/a² ×2ab/[-(a-2b)]
=2