Question

已知3a²+ab-2b²=0，求(b分之a)-a分之b)-(ab分之a²+b²）值

Answer 1

a/b-b/a-(a^2+b^2)/ab
=(a^2-b^2-a^2-b^2)/ab
=-2b^2/ab
=-2b/a

3a^2+ab-2b^2=0
(3a-2b)(a+b)=0
a=2b/3或a=-b
所以原式=-3或2

Answer 2

3a²+ab-2b²=(3a-2b)(a+b)=0
3a-2b=0或a+b=0

3a-2b=0时，
3a=2b,a=2b/3
a/b-b/a-(a²+b²)/ab
=2/3-3/2+(4/9+1)/(2/3)
=4/6-9/6-13/6
=-3

a+b=0时，a=-b
a/b-b/a-(a²+b²)/ab
=-1-(-1)+2
=2