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：作业帮时间：2024/04/28 18:30:18

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

2a²b(a-b)+ab(a-b)²+4ab²(a-b) 化简(a^2-4ab^2+b)/b-(a+b)(a-b) 化简 (a+b/a^2b-ab^2 -4/a^2-b^2) ÷a^2-2ab+b^2/a^2b-ab^2=? 化简[4/(a^2-b^2)+(a+b)/(ab^2-a^2b)]除以(a^2-2ab+b^2)/(a^2b-ab^2) a+b/2ab 2AB/A+B a+b/2ab 4ab/b^2(a-b)= 化简[(a-b)/(a+2b)]/[(a^2-b^2)/(a^2+4ab+b^2)]-(3a^2-4ab)/(a^2+ab) a-b/a^2+ab / ab-a^2/a^2b^2-b^4快化简（a-b+4)(a²-2ab-b²-4a+4b+16）化简(a+b/a^2b-ab^2-4/a^2-b^2)÷a^2-2ab+b^2/a^2-ab^2 已知a0,化简|a|-|b|+|a+b|+|ab|等于A.-ab B. 2a+2b+abC.-2a-2b+ab D.-2a+ab 化简a/(a-b)-b/(a+b)+(2ab)/(a^2-b^2) (a-b)平方-2ab(b-a) (a-b)^3+2ab(a-b) 有理数ab满足a+b＜0.化简|a+b|+(-a)+(-b)+2a+2b 化简a-b分之a+a+b分之b+b平方-a平方分之2ab