化简 (a+b/a^2b-ab^2 -4/a^2-b^2) ÷a^2-2ab+b^2/a^2b-ab^2=?

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/20 00:51:32
化简(a+b/a^2b-ab^2-4/a^2-b^2)÷a^2-2ab+b^2/a^2b-ab^2=?化简(a+b/a^2b-ab^2-4/a^2-b^2)÷a^2-2ab+b^2/a^2b-ab^2

化简 (a+b/a^2b-ab^2 -4/a^2-b^2) ÷a^2-2ab+b^2/a^2b-ab^2=?
化简 (a+b/a^2b-ab^2 -4/a^2-b^2) ÷a^2-2ab+b^2/a^2b-ab^2=?

化简 (a+b/a^2b-ab^2 -4/a^2-b^2) ÷a^2-2ab+b^2/a^2b-ab^2=?
原式=[(a+b)/(a^2b-ab^2)-4/(a^2-b^2)]×[(a^2b-ab^2)/(a-b)^2]
=(a+b)/(a^2b-ab^2)×[(a^2b-ab^2)/(a-b)^2]-4/(a^2-b^2)×[(a^2b-ab^2)/(a-b)^2]
=(a+b)//(a-b)^2-4ab(a-b)/(a+b)(a-b)^3
=(a+b)//(a-b)^2-4ab/(a+b)(a-b)^2
=[(a+b)^2-4ab]/(a+b)(a-b)^2
=[(a^2+2ab+b^2-4ab]/(a+b)(a-b)^2
=(a^2-2ab+b^2)/(a+b)(a-b)^2
=(a-b)^2/(a+b)(a-b)^2
=1/(a+b)


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

全部展开


原式=[(a+b)/(a^2b-ab^2)-4/(a^2-b^2)]×[(a^2b-ab^2)/(a-b)^2]
=(a+b)/(a^2b-ab^2)×[(a^2b-ab^2)/(a-b)^2]-4/(a^2-b^2)×[(a^2b-ab^2)/(a-b)^2]
=(a+b)//(a-b)^2-4ab(a-b)/(a+b)(a-b)^3
=(a+b)//(a-b)^2-4ab/(a+b)(a-b)^2
=[(a+b)^2-4ab]/(a+b)(a-b)^2
=[(a^2+2ab+b^2-4ab]/(a+b)(a-b)^2
=(a^2-2ab+b^2)/(a+b)(a-b)^2
=(a-b)^2/(a+b)(a-b)^2
=1/(a+b)
希望您能看懂,祝你学习进步

收起