已知2x²-xy-3y²=0,求x-y/x+y

已知2x²-xy-3y²=0,求x-y/x+y
已知2x²-xy-3y²=0,求x-y/x+y

已知2x²-xy-3y²=0,求x-y/x+y
解
2x²-xy-3y²=0
(2x-3y)(x+y)=0
当2x-3y=0时
x=3/2y
∴(x-y)/(x+y)
=(3/2y-y)/(3/2y+y)
=(1/2)/(5/2)
=1/5
当x+y=0时,不成立
∴(x-y)/(x+y)=1/5

2x^2-xy-3y^2=(2x-3y)(x+y)=0
得2x-3y=0 或x+y=0
所以2x=3y
所以(x-y)/(x+y)
=(x-2/3 x)/(x+2/3 x)
=1/3 /(5/3)
=1/5

2x²-xy-3y²=0
(2x-3y)(x+y)=0
若x+y=0时，所求式分母为0，无意义
所以x+y≠0
2x-3y=0
y=2x/3
于是
x-y\x+y
=(x-2x/3)/(x+2x/3)
=x/3 / (5x/3)
=1/5

2x²-xy-3y²=0
(2x-3y)(x+y)=0
2x-3y=0,即x=3y/2或x+y=0
(x-y)/(x+y)=1/5