已知1/a-1/b=5,则(2a+3ab-2b)/(a-2ab-b)=?

题目

已知1/a-1/b=5,则(2a+3ab-2b)/(a-2ab-b)=?

答案

1/a-1/b=(b-a)/ab=5
b-a=5ab
a-b=-5ab
(2a+3ab-2b)/(a-2ab-b)
=[2(a-b)+3ab]/[(a-b)-2ab]
=(-10ab+3ab)/(-5ab-2ab)
=-7ab/(-7ab)
=1