b/a+a/b=3,求2ab/(a*a+b*b)-(3a*a+ab+3b*b)/2ab的值

题目

b/a+a/b=3,求2ab/(a*a+b*b)-(3a*a+ab+3b*b)/2ab的值

答案

因为b/a+a/b=3
所以a²+b²=3ab
那么 2ab/（a*a+b*b)-(3a*a+ab+3b*b)/2ab
=2ab/3ab-(9ab+ab)/2ab
=-13/3