Question

化简[(a-b)/(a+2b)]/[(a^2-b^2)/(a^2+4ab+b^2)]-(3a^2-4ab)/(a^2+ab)

Answer 1

解: [(a-b)/(a+2b)]/[(a^2-b^2)/(a^2+4ab+b^2)]-(3a^2-4ab)/(a^2+ab)
= [(a-b)/(a+2b)]*[(a²+4ab+b²)/(a²-b²)]-(3a²-4ab)/(a²+ab)
=[(a-b)/(a+2b)]*{(a²+4ab+b²)/[(a+b)(a-b)]}-(3a-4b)/(a+b)
=(a²+4ab+b²)/[(a+2b)(a+b)]-[(3a-4b)(a+2b)]/[(a+b)(a+2b)]
=[(a²+4ab+b²-(3a-4b)(a+2b)]/[(a+b)(a+2b)]
=[a²+4ab+b²-(3a²+6ab-4ab-8b²)]/(a²+2ab+ab+2b²)
=(a²+4ab+b²-3a²-2ab+8b²)/(a²+3ab+2b²)
=(-2a²+2ab+9b²)/(a²+3ab+2b²)
祝你学习进步,如有不明可以追问.同意我的答案请采纳,O(∩_∩)O谢谢

Answer 2

[(a-b)/(a+2b)]/[(a^2-b^2)/(a^2+4ab+4b^2)]-(3a^2-4ab)/(a^2+ab)
=[(a-b)/(a+2b)]×[(a+2b)²/(a-b)(a+b)]-(3a²-4ab)/(a²+ab)
=(a+2b)/(a+b)-a(3a-4b)/a(a+b)
=(a+2b)/(a+b)-(3a-4b)/(a+b)
=(a+2b-3a+4b)/(a+b)
=(-2a+6b)/(a+b)