(x^-2-y^-2)÷(x^-1+y^-1)+1/y-1/x
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(x^-2-y^-2)÷(x^-1+y^-1)+1/y-1/x
(x^-2-y^-2)÷(x^-1+y^-1)+1/y-1/x
(x^-2-y^-2)÷(x^-1+y^-1)+1/y-1/x
=(1/x^2-1/y^2)/(1/x+1/y)+1/y-1/x
=[(1/x+1/y)(1/x-1/y)]/(1/x+1/y)+1/y-1/x
=(1/x-1/y)+1/y-1/x
=0
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