Question

Aratati ca: (2/x-2+ x/ x+2) : x²+4/x²-x-2=x+1/x+2

Answer 1

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