If X=(Y+1)/(Y-2), multiply both sides by (Y-2) to give X(Y-2) = Y+1. Multiply out, XY - 2X = Y+1. Now gather all the terms involving Y together onto one side and all the terms not involving Y onto the other. XY - Y = 1 + 2X. Factorise, Y(X-1) = 2X+1. Now divide through: Y = (2X+1)/(X-1).