Let x=a||b be a "balance number" (so that a and b are positive rational numbers, or 0). Show that x can be expressed in one of two simplified forms: Either

x= c||0 (for some rational number c >= 0), or Let x = 0 ]d (for some rational d > 0). Express c and d in terms of a and b. When can x be expressed in the first form, and when can it be expressed in the second? Is it possible for a given x to be expressible in both forms? Explain.