Question

x/x+2-(x-2)²/2* (1/x²-4 +1/x²-4x+4)=

Answer 1

x/(x+2) - (x-2)²/2 * (1/(x²-4) +1/(x²-4x+4)) =
=  x/(x+2) - (x-2)²/2 * (1/(x-2)(x+2) +1/(x-2)²) =
=  x/(x+2) - (x-2)²/2 * ((x-2)/(x-2)²(x+2) +  (x+2)/(x-2)²(x+2)) =
=  x/(x+2) - (x-2)²/2 * (x-2 + x+2)/(x-2)²(x+2)  =
=  x/(x+2) - (x-2)²/2 *  2x/(x-2)²(x+2)  =
=  x/(x+2)  -   ((x-2)² *2x ) / 2(x-2)²(x+2)  =
=  x/(x+2)  -  x/(x+2)  =  0