化简求值x/(x+y)+y/(x-y)-2xy/(x^2-y^2),其中x=5,y=2

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化简求值x/(x+y)+y/(x-y)-2xy/(x^2-y^2),其中x=5,y=2
化简求值x/(x+y)+y/(x-y)-2xy/(x^2-y^2),其中x=5,y=2

化简求值x/(x+y)+y/(x-y)-2xy/(x^2-y^2),其中x=5,y=2
x/(x+y)+y/(x-y)-2xy/(x^2-y^2)
=x*(x-y)/(x+y)(x-y)+y*(x+y)-2xy/(x^2-y^2)
=(x^2-xy)/(x^2-y^2)+(xy+y^2)/(x^2-y^2)-2xy/(x^2-y^2)
=(x^2+y^2-2xy)/(x^2-y^2)
=(x-y)/(x+y)
代入X=5,Y=2得
(5-2)/(5+2)
=3/7

x/(x+y)+y/(x-y)-2xy/(x^2-y^2)
=x(x-y)+y(x+y)-2xy /(x^2-y^2)
=(x-y)^2/(X-y)(x+y)
=(x-y)/(x+y)
带入x=5,y=2
得3/7