观察等式\(2 - \frac{1}{3} = 2 \times \frac{1}{3} + 1\)，\(5 - \frac{2}{3} = 5 \times \frac{2}{3} + 1\)，给出如下定义：我们称使等式\(a - b = a \cdot b + 1\)成立的一对有理数\(a\)，\(b\)为“共生有理数对”，记为\((a,b)\)，如：数对\((2,\frac{1}{3})\)，\((5,\frac{2}{3})\)都是“共生有理数对”．
\( - 2 - 1 = - 3\)，\( - 2 \times 1 + 1 = - 1\)
\(\therefore - 2 - 1 \ne - 2 \times 1 + 1\)
\(\therefore ( - 2,1)\)不是“共生有理数对”
\(\because 3 - ( - \frac{1}{2}) = \frac{7}{2}\)，\(3 \times ( - \frac{1}{2}) + 1 = - \frac{1}{2}\)
\(\therefore 3 - ( - \frac{1}{2}) \ne 3 \times ( - \frac{1}{2}) + 1\)
\(\therefore (3, - \frac{1}{2})\)不是“共生有理数对”
