作业帮化简[(a-b)/(a+2b)]/[(a^2-b^2)/(a^2+4ab+b^2)]-(3a^2-4ab)/(a^2+a
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/17 05:47:59
化简[(a-b)/(a+2b)]/[(a^2-b^2)/(a^2+4ab+b^2)]-(3a^2-4ab)/(a^2+ab)
[(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)
= [(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)
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