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

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

b/(a^2-ab)+c/(b^2-ab)+(a+b^2)/(a^2b-ab^2)
b/(a^2-ab)+c/(b^2-ab)+(a+b^2)/(a^2b-ab^2)
=b/[a(a-b)]+c/[b(b-a)]+(a+b²)/[ab(a-b)]
=b/[a(a-b)]-c/[b(a-b)]+(a+b²)/[ab(a-b)]
=[ab-ac+(a+b²)]/[ab(a-b)]
=(ab-ac+a+b²)/[ab(a-b)]