Question

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

Answer 1

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