Solve the following equation Show all your work xx2 x 1x

Solve the following equation. Show all your work. x/x-2 + x - 1/x + 1 = -1

x/(x -2) + (x -1)/ ( x + 1) = [1/(x-2)(x +1) ] [ x(x+1) + (x -1)(x -2)] = [1/(x-2)(x +1)] ( x²+ x + x² -3 x +2} = [1/(x-2)(x +1)]( 2x² -2x +2) = [ 2/(x -2)(x+1)](x² -x +1) = 2(x² -x +1)/(x -2)(x+1) = 2(x² -x +1)/ ( x² -x -2)