已知2x=3y,求(xy/x^2+y^2)-(y^2/x^2-y^2)的值

题目

已知2x=3y,求(xy/x^2+y^2)-(y^2/x^2-y^2)的值
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答案

2x=3y
y=2/3x
(xy/x^2+y^2)-(y^2/x^2-y^2)
=x*2/3x/(x^2+4/9x^2)-4/9x^2/(x^2-4/9x^2)
=6/13-4/5
=-22/65