计算:(4xy(x-y)^-1+(x(y^-1)-(x^-1)y)/((x^-1)+(y^-1)))*(x+y)^-2

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计算:(4xy(x-y)^-1+(x(y^-1)-(x^-1)y)/((x^-1)+(y^-1)))*(x+y)^-2

计算:(4xy(x-y)^-1+(x(y^-1)-(x^-1)y)/((x^-1)+(y^-1)))*(x+y)^-2
计算:(4xy(x-y)^-1+(x(y^-1)-(x^-1)y)/((x^-1)+(y^-1)))*(x+y)^-2

计算:(4xy(x-y)^-1+(x(y^-1)-(x^-1)y)/((x^-1)+(y^-1)))*(x+y)^-2
原式
=[4xy/(x-y)+(x/y-y/x)/(1/x+1/y)]/(x+y)^2
=[4xy/(x-y)+(x^2-y^2)/(y+x)]/(x+y)^2
=[4xy/(x-y)+(x-y)]/(x+y)^2
=[4xy+(x-y)^2]/[(x-y)(x+y)^2]
=(x+y)^2/[(x-y)(x+y)^2]
=1/(x-y)