elementary number theory - If $aleq b$ then $bc+1$ does not divide $ab$.

Here is my problem:

Let $a,b,c$ be positive integers such that $a\leq b$. Show that $bc+1$ does not divide $ab$.

First I thought I could show that $\frac{ab}{bc+1}<1$, but this is not necessarily. I am trying to express it as $\frac{ab}{bc+1}=x+\frac{p}{q}$ where $x$ is an integer and then show that $\frac{p}{q}\neq 0$, but I am unable to do so.