# Multiplying with variable

#### Mr. Bland

##### Junior Member
In a formal sense, it should be noted that $$\displaystyle U \ne 0$$ due to the potential for zero division. Your teacher was demonstrating that a fraction in the form of $$\displaystyle \frac{x}{x} = 1$$, which of course doesn't apply to zero anyway because $$\displaystyle \frac{0}{0}$$ isn't a valid fraction.

In other cases, such as $$\displaystyle \left(\sqrt{x}\right)^2 = x$$, it's important to understand that there is a range of valid possibilities, but depending on the context it may be inconvenient or "too wordy" to spell it all out every time. The focus is the on relationship between $$\displaystyle \sqrt{x}$$ and $$\displaystyle x^2$$, not on the fact that $$\displaystyle \sqrt{x}$$ expects and returns non-negative values.

• Ryan$#### Ryan$

##### Full Member
Yes, we need to note that U can't be zero. Maybe it's clear from the context that U can't be 0?
that what I want to verify, if from the context it's clear that we are not meaning 0/0 .. then we can not writing a note that variable can't be zero over variable/variable? if from context we can assume that and this assumption is logically considered right, then fine for me and now it's obvious why they are neglecting a note when dividing X/X or VARIABLE/VARIABLE

#### JeffM

##### Elite Member
that what I want to verify, if from the context it's clear that we are not meaning 0/0 .. then we can not writing a note that variable can't be zero over variable/variable? if from context we can assume that and this assumption is logically considered right, then fine for me and now it's obvious why they are neglecting a note when dividing X/X or VARIABLE/VARIABLE
I still think it is a bit sloppy

• Jomo

#### mmm4444bot

##### Super Moderator
Staff member
… is it right to multiply U/U on formula I=U/R without saying that U can't be zero? …
$$\;$$
Fair enough if it is obvious that U $$\displaystyle \neq$$0 then one can get away without saying that U $$\displaystyle \neq$$0 when multiplying by U/U. Otherwise it is sloppy not to mention it. I have this obsession that equal signs MUST be valid and when they are not your work is not (completely) correct.