x+2y+4y^2/x-2y-4x^2y/x^2-4y^2

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x+2y+4y^2/x-2y-4x^2y/x^2-4y^2
x+2y+4y^2/x-2y-4x^2y/x^2-4y^2

x+2y+4y^2/x-2y-4x^2y/x^2-4y^2
x+2y+4y^2/(x-2y) -4x^2y/(x^2-4y^2)
=[(x+2y)(x-2y)+4y²]/(x-2y) -4x^2y/(x^2-4y^2) 前面的通分
=x²/(x-2y)-4x^2y/(x^2-4y^2)
=[x²(x+2y)-4x²y/(x²-4y²)
=x²(x-2y)/(x+2y)(x-2y)
=x²/(x+2y)