120/(x-y)+120/(x+y)=160/y 怎样化简成x=2y和x=-1/2y

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120/(x-y)+120/(x+y)=160/y 怎样化简成x=2y和x=-1/2y
120/(x-y)+120/(x+y)=160/y 怎样化简成x=2y和x=-1/2y

120/(x-y)+120/(x+y)=160/y 怎样化简成x=2y和x=-1/2y
两边同时乘以y(x-y)(x+y),得
120y(x+y)+120y(x-y)=160(x-y)(x+y)
3xy+3y^2+3xy-3y^2=4x^2-4y^2
2x^2-3xy-2y^2=0
(2x+y)(x-2y)=0
x=2y或x=-1/2y