Question (d): Infinite domain III (20 pts) Suppose a, b and c are integers (Z), while x, y and z are non-zero reals (R 6=0). If the following relations hold for these numbers: a = x · y x + y b = x · z x + z c = y · z y + z prove that x, (not necessarily y or z) is a rational number (Q). Some hints: (i) How can you prove that a certain number is rational? (ii) Can a, b or c be zero? Why? You would have to mention why if you need to show us that they are non-zero! (iii) If you see yourself doing a lot of algebra... keep going! Find a way to get x alone and integers on the other side of the equality.