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