In the following function : $$f(x)= \frac{(x^2+3x)}{x}$$ Why there's an undefined value when $x=0$, since we can simplified the formula as $$f(x)= \frac{x(x+3)}{x}$$ Then cancel out the common factor $x$, we can get $$f(x)=x+3$$ In this situation, all the value is defined, but why in the unsimplified formula we have an undefined value when $x=0$?
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Original function was valid when $x \ne 0$. When you cancel the $x$ , you are claiming that $x \ne 0$. Hence when you get the New function , you still have to use $x \ne 0$ & you can not use $x=0$ to get $f(0)$. Hence , those two functions are still equal where-ever it matters ! – Prem Dec 08 '23 at 07:55