y/(x+y)-x/(x-y)
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y/(x+y)-x/(x-y)
![y/(x+y)-x/(x-y)](/uploads/image/z/19863529-25-9.jpg?t=y%2F%28x%2By%29-x%2F%28x-y%29)
y/(x+y)-x/(x-y)
=y(x-y) /(x+y)(x-y) -x(x+y) /(x+y) (x-y)
=[y(x-y) -x(x+y)] /(x+y) (x-y)
=[xy-y^2 -x^2-xy] /(x+y) (x-y)
=[-y^2-x^2] /(x+y) (x-y)
=-(x^2+y^2)/(x^2-y^2)
=y(x-y) /(x+y)(x-y) -x(x+y) /(x+y) (x-y)
=[y(x-y) -x(x+y)] /(x+y) (x-y)
=[xy-y^2 -x^2-xy] /(x+y) (x-y)
=[-y^2-x^2] /(x+y) (x-y)
=-(x^2+y^2)/(x^2-y^2)