(x+1)/(x-1)-(x-2x)/(x-1)÷[(x-x-2)/(x+2x+1)] =(x+1)/(x-1)-x(x-2)/(x-1)÷[(x-2)(x+1)/(x+1)] =(x+1)/(x-1)-x(x-2)/[(x+1)(x-1)]÷[(x-2)/(x+1)] =(x+1)/(x-1)-x/(x-1) =1/(x-1)
