已知2x²+3xy-2y²=0(xy≠0),求(x+y)/(x-y)的值

题目

已知2x²+3xy-2y²=0(xy≠0),求(x+y)/(x-y)的值

答案

2x²+3xy-2y²=0
(2x-y)(x+2y)=0
y=2x,x=-2y
当y=2x时,
(x+y)/(x-y)
=(x+2x)/(x-2x)
=-3
当x=-2y时,
(x+y)/(x-y)
=(-2y+y)/(-2y-y)
=1/3