Упростите выражение: 5/1+4x^-1(x-4/x^2+4x-16/16-x^2)

[latex] \frac{5}{1+4x^{-1}} * ( \frac{x-4}{x^2+4x} + \frac{4x-16}{16-x^2} ) = \frac{5}{1+4x^{-1}} * ( \frac{x-4}{x(x+4)} + \frac{4(x-4)}{-(x-4)(x+4))} )= \\ \\ =\frac{5}{1+4x^{-1}} *( \frac{x-4}{x(x+4)} - \frac{4}{x+4} ) = \frac{5}{1+4x^{-1}} * \frac{x-4-4x}{x(x+4)} = [/latex] [latex] =\frac{5}{1+ \frac{4}{x} } * (- \frac{4+3x}{x^2+4x} ) = - \frac{5(4+3x)}{(1+ \frac{4}{x}) (x^2+4x)} = \\ \\ = -\frac{20+15x}{x^2+4x+4x+16} =- \frac{20+15x}{x^2+8x+16} = -\frac{20+15x}{(x+4)^2} [/latex]