$\dfrac{\text{Irrational}}{\text{Irrational}} = ?$

Note that $\pi$ is irrational and so is $2\pi$ . But $\dfrac \pi{2\pi} = \dfrac 12$ is rational. Therefore, the statement is false ,

$\dfrac{\sqrt3}{\sqrt3}=1$

The simplest thing is to think that any nonzero number divided by itself is 1.

$\huge \frac{\tau}{\pi} = 2$

$\large \frac{\sqrt{2}}{\sqrt{2}}= 1$

Note: 1 is rational while square root of 2 is irrational