已知非零整数a,b,满足ab=a-b,求a/b+b/a-ab

题目

已知非零整数a,b,满足ab=a-b,求a/b+b/a-ab

答案

a/b+b/a-ab
=（aa+bb)/ab-ab
=[(a-b)(a-b)+2ab]/ab-ab
=(abab+2ab)/ab-ab
=ab+2-ab
=2