Algebraic expressions

first of all lets evaluate a bit:

 

$ \frac{a+3}{a^3-a} $

 

$ \frac{a+3}{a\left(a^2-1\right) } $

 

$ \frac{a+3}{a\left(a+1\right)\left(a-1\right)}  $

 

now, any rational expression will be undefined when the denominator is $=\: 0$ right? because dividing by 0 ( consider it like like something which does not exist ) just makes no sense. so we note that when $a\left(a+1\right)\left(a-1\right)=0$, that expression is undefined:

 

$a\left(a+1\right)\left(a-1\right)=0$

 

 

$ \left(a+1\right)\left(a-1\right)=\frac{0}{a}  $

 

$  \left(a+1\right)\left(a-1\right)=0   $       $ \implies \begin{cases} a+1=0  \\ \ \ \ \ \text{and}  \\ a-1=0   \end{cases} \implies \begin{cases} a=-1  \\ \ \ \text{and}  \\ a=1   \end{cases}   $  

 

thus, whenever $\boxed{a=1,\: -1}$ the fraction becomes undefined