Simplifying a fraction with the divisibility

Euclidean algorithm.
\begin{align*}
1995 &= 1\cdot1785+210,\\
1785 &= 8\cdot210+105,\\
210 &= 2\cdot105+0.
\end{align*}
So $\divisibility(1725,1995)=105$.

Simplification.
$$\frac{1725}{1995}=\frac{1725/105}{1995/105}=\frac{17}{19}.$$

Since $17$ is prime and does not divide $19$, the fraction is irreducible.