已知2x=3y,求(xy/x^2+y^2)-(y^2/x^2-y^2)的值帮帮忙!

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已知2x=3y,求(xy/x^2+y^2)-(y^2/x^2-y^2)的值帮帮忙!
已知2x=3y,求(xy/x^2+y^2)-(y^2/x^2-y^2)的值
帮帮忙!

已知2x=3y,求(xy/x^2+y^2)-(y^2/x^2-y^2)的值帮帮忙!
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

楼上的,应先化简呀!
先通分,再化为[ xy ( x^2 - y^2 ) - y^2 ( x^2 + y^2 ) ] / ( x^2 - y^2 ) * ( x^2 + y^2 )
再分开,化为 xy / ( x^2 + y^2 ) - y^2 / ( x - y ) ( x + y )
再将2x = 3y化为 x = ( 3 / 2 ) y 代入,得
[ ( 3 ...

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楼上的,应先化简呀!
先通分,再化为[ xy ( x^2 - y^2 ) - y^2 ( x^2 + y^2 ) ] / ( x^2 - y^2 ) * ( x^2 + y^2 )
再分开,化为 xy / ( x^2 + y^2 ) - y^2 / ( x - y ) ( x + y )
再将2x = 3y化为 x = ( 3 / 2 ) y 代入,得
[ ( 3 / 2 ) y^2 ] / [ ( 13 / 4 ) y^2 ] - y^2 / ( 5 / 4 ) y^2
= 6 / 13 - 4 / 5
= - 22 / 65

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