设x,y是实数,要使分式(x^2-xy-2y^2)/(x^2-y^2)的值等于零,x,y应满足怎样的条件

题目

设x,y是实数,要使分式(x^2-xy-2y^2)/(x^2-y^2)的值等于零,x,y应满足怎样的条件

答案

(x^2-xy-2y^2)/(x^2-y^2)的值等于零
x^2-xy-2y^2=0
(x-2y)(x+y)=0
x-2y=0或x+y=0
x=2y,x= -y(舍去)
x=2y时,分式(x^2-xy-2y^2)/(x^2-y^2)的值等于零