Question

$( frac{x}{ x^{2}-4}+ frac{2}{2-x} + frac{1}{2+x}):(x-2+ frac{10 -x^{2} }{2+x})$

Answer 1

$( frac{x}{ x^{2}-4}+ frac{2}{2-x} + frac{1}{2+x}):(x-2+ frac{10 -x^{2} }{2+x})=$
$=( frac{x}{(x-2)(x+2)}- frac{2}{x-2}+ frac{1}{x+2} ): frac{(x-2)(x+2)+10-x^2}{x+2} =$
$=frac{x-2(x+2)+x-2}{(x-2)(x+2)}* frac{x+2}{x^2-4+10-x^2}= frac{-4-2}{x-2}* frac{1}{-4+10}=- frac{1}{x-2}= frac{1}{2-x}$