已知1/a+1/b=3,则分式(a+3ab+b)/(a-2ab+b)的值是( )

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已知1/a+1/b=3,则分式(a+3ab+b)/(a-2ab+b)的值是( )
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已知1/a+1/b=3,则分式(a+3ab+b)/(a-2ab+b)的值是( )
已知1/a+1/b=3,则分式(a+3ab+b)/(a-2ab+b)的值是( )

已知1/a+1/b=3,则分式(a+3ab+b)/(a-2ab+b)的值是( )
(a+3ab+b)/(a-2ab+b)
分子分母同除以ab得:
(1/b+1/a+3)/(1/b+1/a-2)
=(3+3)/(3-2)
=6

1/a+1/b=3
(a+b)/ab=3
3ab=a+b
ab=(a+b)/3
(a+3ab+b)/(a-2ab+b)
=2(a+b)/[a+b-2(a+b)/3]
=2/(1-2/3)
=6

(a+3ab+b)/(a-2ab+b)
分子分母同除以ab得:
(1/b+1/a+3)/(1/b+1/a-2)
=(3+3)/(3-2)