Question

一道数学通分题

x-y/2x+2y与xy/(x+y)²
写出过程

Answer 1

x-y/2x+2y
=(2x^2-y+2xy)/2x
=(2x^2-y+2xy)(x+y)^2/2x(x+y)^2
xy/(x+y)^2
=2x*xy/2x(x+y)^2

Answer 2

(x-y)/2(x+y) = (x-y)(x+y)/2(x+y)^2 = (x^2-y^2)/2(x+y)^2
xy/(x+y)^2 = 2xy/2(x+y)^2
因为(x-y)/2(x+y) - xy/(x+y)^2 = (x^2-2xy-y^2)/2(x+y)^2 = [(x-y)^2 - 2y^2]/2(x+y)^2
所以 无法比较大小。