How to prove that a polynomial with leading coefficient $1$ has no fractional solutions

Question

I want to prove that the equation $$x^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+\dots+a_0=0$$ has no solutions in the form of $p/q$ when $p$ and $q$ and coprime and $q>1$. With this polynomial, $a_n=1$ and $a_i$ is an integer. I have already proven this; I want to see how other people prove it.