(x/x-2-x/x+2)/4x/x-2

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(x/x-2-x/x+2)/4x/x-2

(x/x-2-x/x+2)/4x/x-2
(x/x-2-x/x+2)/4x/x-2

(x/x-2-x/x+2)/4x/x-2
(x/x-2-x/x+2)÷ 4x/x-2
=[x(x+2)-x(x-2)]/(x+2)(x-2)×(x-2)/4x
=4x/(x+2)(x-2) ×(x-2)/4x
=1/(x+2)