[2x/(x2-4)-1/(x-2)]·(x+2)/(x-1)
=[2x/(x+2)(x-2)-1/(x-2)]*(x+2)/(x-1)
=(2x-x-2)/(x+2)(x-2)*(x+2)/(x-1)
=1/(x+2)*(x+2)/(x-1)
=1/(x-1)