(x^2-4y^2/x^2+4x+4)*(x+2/3x^2+6xy)

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(x^2-4y^2/x^2+4x+4)*(x+2/3x^2+6xy)

(x^2-4y^2/x^2+4x+4)*(x+2/3x^2+6xy)
=(x+2y)(x-2y)/(x+2)^2 *(x+2/3x(x+2y))
=(x-2y)/3x(x+2)