已知1/a-1/b=3,求分式2a+3ab-2b/a-ab-b的值

题目

已知1/a-1/b=3,求分式2a+3ab-2b/a-ab-b的值

答案

1/a-1/b=3
(b-a)/ab=3
b-a=3ab
2a+3ab-2b/a-ab-b
=(2a+b-a-2b)[a-b-(b-a)/3]
=(a-b)/[4(a-b)/3]
=3/4
或者
2a+3ab-2b/a-ab-b
=[2(-3ab)+3ab]/(-3ab-ab)
=3/4