Question 15
Let \(\mathbb Q\) and \(\mathbb N^*\) be the rational numbers and positive integers. Suppose \((ax+b)/x\in\mathbb Q\) for every \(x\in\mathbb N^*\). Prove that there are integers \(A,B,C\) such that \(\frac{ax+b}{x}=\frac{Ax+B}{Cx}\) for every \(x\in\mathbb N^*\).