已知x/y=1/2,求分式（x²+2xy+y²）/（x-2y）（x+y）的值

题目

已知x/y=1/2,求分式（x²+2xy+y²）/（x-2y）（x+y）的值

答案

由x/y=1/2得：y=2x,
(x²+2xy+y²/(x-2y)(x+y) = x+y)²/(x-2y)(x+y) = x+y)/(x-2y) = (x+2x)/(x-4x) = 3x/(-3x) = -1