I have done quite a few exercises, and I have never considered some restrictions, for example:
For m $\neq 0$ , $\dfrac{m+n}{m} - \dfrac{n-m}{m}$
Resolving:
= $\dfrac{m + n - n + m}{m}$ = $\dfrac{2m}{m} = 2$
Well, the answer is correct. I even arrived at the result, regardless of the restriction. What is that restriction telling me? if $m = 0$, the result is erroneous? Or if the result was $0$, is it wrong?
Besides this, do you have practical exercises where to apply these rules is totally fundamental to solve exercises? (Consider that I am a school student yet)
Dividing any number by zero does not make sense. In this case $m\neq 0$ is necessary for the statement to even have any meaning. In other cases the restrictions may be necessary for certain steps in the resolution.
Edit: one example of this is the following: suppose $xm = 5m$, what is the value of $x$? If $m\neq 0$ you can divide by $m$ and conclude $x=5$, but if $m=0$ not only this step would be wrong but also $x$ can have any value, as $1\times 0 = 5\times 0 = \pi \times 0= \cdots$.