x+1/x-2 - x-1/x+2=2 (x^2+2)/x^2-4

(x+1)(x+2)/(x+2)(x-2) - (x-1)(x-2)/(x+2)(x-2)=2( x²+2)/(x+2)(x-2)

<=>(x+1)(x+2)-(x-1)(x-2)/(x+2)(x-2)=2( x²+2)/(x+2)(x-2)

<=> (x²+3x+2-x²+3x-2)/(x+2)(x-2) - 2( x²+2)/(x+2)(x-2)=0             ĐKXĐ: x$\neq$ ±2

<=> 6x-2x²-4/(x+2)(x-2)=0

=> -(2x²-6x+4)=0

<=> -2(x²-3x+2)=0

=> x²-3x+2=0

      x²-x-2x+2=0

      (x-2)(x-1)=0

=>ta có 2TH

TH1: x-2=0

        x=2( KTMĐK)

TH2: x-1=0

      x=1