如果2x+y=0,xy不等于0,那么分式x^2+2xy/xy+y^2的值为

Question

如果2x+y=0,xy不等于0,那么分式x^2+2xy/xy+y^2的值为

Answer 1

2x+y=0
解得,y= -2x
(x^2+2xy)/(xy+y^2)
=[x^2+2x·(-2x)]/[x·(-2x)+(-2x)^2]
=(-3x^2)/(2x^2)
=-3/2