[math-fun] Rational mapping puzzle

Puzzle: ------- Let D in R^2 denote the open unit disk {(x,y) | x^2 + y^2 < 1} Let J denote the interval [0,1) x {0} in R^2. Find a rational mapping f(x,y) = P(x,y) / Q(x,y) taking D onto its subset D - J and prove that this holds. —Dan