已知1/a+1/b=2/3,求代数式[a/(a+b)-b/(b-a)-2ab/(a2-b2)除以(1/a-1/b)的值

已知1/a+1/b=2/3,求代数式[a/(a+b)-b/(b-a)-2ab/(a2-b2)除以(1/a-1/b)的值
已知1/a+1/b=2/3,求代数式[a/(a+b)-b/(b-a)-2ab/(a2-b2)除以(1/a-1/b)的值

已知1/a+1/b=2/3,求代数式[a/(a+b)-b/(b-a)-2ab/(a2-b2)除以(1/a-1/b)的值
1/a+1/b=2/3
[a/(a+b)-b/(b-a)-2ab/(a2-b2)] /(1/a-1/b)
= [a/(a+b)+b/(a-b)-2ab/(a2-b2)] / [(b-a)/(ab)]
= { [a(a-b)+b(a+b)-2ab]/(a2-b2)] } / [-(a-b)/(ab)]
= { a^2-ab+ab+b^2-2ab]/(a2-b2)] } / [-(a-b)/(ab)]
= -(a-b)^2/(a+b)(a-b) * ab/(a-b)
= -ab/(a+b)
= -1/(1/a+1/b)
= -1/(2/3)
= -3/2

1/a+1/b=2/3 (a+b)/ab=2/3
[a/(a+b)-b/(b-a)-2ab/(a2-b2)=[(a^2+b^2)/(a^2-b^2)]-2ab/(a2-b2)=(a-b)^2/(a^2-b^2)=(a-b)/(a+b)
(1/a-1/b)=(b-a)/ab
代数式[a/(a+b)-b/(b-a)-2ab/(a2-b2)除以(1/a-1/b)
=-ab/(a+b)
=-3/2

[a/(a+b)-b/(b-a)-2ab/(a2-b2)] /(1/a-1/b)
= [a/(a+b)+b/(a-b)-2ab/(a2-b2)] / [(b-a)/(ab)]
= { [a(a-b)+b(a+b)-2ab]/(a2-b2)] } / [-(a-b)/(ab)]
= { a^2-ab+ab+b^2-2ab]/(a2-b2)] } / [-(a-b)/(ab)]
= -(a-b)^2/(a+b)(a-b) * ab/(a-b)
= -ab/(a+b)
= -(1/a+1/b)
= -2/3

[a/(a+b)-b/(b-a)-2ab/(a2-b2)除以(1/a-1/b)
=[(a^2+b^2)/(a2-b2)-2ab/(a2-b2)]除以[(b-a)/ab]
=(a-b)^2/(a2-b2)]除以[(b-a)/ab]
=(b-a)ab/(a2-b2)
=-ab/(a+b)=-3/2