(4x^2-y^2)/(x^2-4y^2)-(2x-y)^2/(x^2-4y^2)-(2y^2-4xy)/(4y^2-x^2)=

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(4x^2-y^2)/(x^2-4y^2)-(2x-y)^2/(x^2-4y^2)-(2y^2-4xy)/(4y^2-x^2)=
(4x^2-y^2)/(x^2-4y^2)-(2x-y)^2/(x^2-4y^2)-(2y^2-4xy)/(4y^2-x^2)=

(4x^2-y^2)/(x^2-4y^2)-(2x-y)^2/(x^2-4y^2)-(2y^2-4xy)/(4y^2-x^2)=
(4x^2-y^2)/(x^2-4y^2)-(2x-y)^2/(x^2-4y^2)-(2y^2-4xy)/(4y^2-x^2)
=(4x²-y²)/(x²-4y²)-(2x-y)²/(x²-4y²)-(4xy-2y²)/(x²-4y²)
=(4x²-y²-4x²+4xy-y²-4xy+2y²)/(x²-4y²)
=0/(x²-4y²)
=0