Question

Выражение (2/x^2-4+1/2x-x^2): 1/x^2+4x+4

Answer 1

$( \frac{2}{x^2-4} + \frac{1}{2x-x^2} ) : \frac{1}{x^2+4x+4} = ( \frac{2}{x^2-2^2} + \frac{1}{-x(x-2)} ) : \frac{1}{x^2+2*2x+2^2}= \\ \\ = (\frac{2}{(x-2)(x+2)} + \frac{1}{-x(x-2)} ) * \frac{(x+2)^2}{1} = \frac{2*(-x) +1(x+2)}{-x(x-2)(x+2)} * \frac{(x+2)^2}{1} = \\ \\ = \frac{-2x+x+2}{-x(x-2)(x+2)} * \frac{(x+2)^2}{1} = \frac{(2-x)(x+2)}{-x(x-2)} = \\ \\ = \frac{-(x-2)(x+2)}{-x(x-2)} = \frac{-(x+2)}{-x} = \frac{x+2}{x} = 1 + \frac{2}{x}$