39. "Proof: Supposer and s are rational numbers. If r + s is rational, then by definition of rational r + s = a/b for some integers a and b with b 0. Also sincer and s are rational, r = i/j and s= m/n for some integers i, j, m, and n with j #0 and n = 0. It follows that i m r+s=+ 'b' which is a quotient of two integers with a nonzero denomi- nator. Hence it is a rational number. This is what was to be shown."