Would this be the right way to plug a "Removable Discontinuity"?

I have this function #f(x)=\frac {x^2-4}{x-2}# and we know that there is a "Hole" when #x => 2#. I need to make this continuous at every #\mathbb {R}#.

Would the representation below be ok?

#f(x) =\begin{cases}\frac {x^2-4}{x-2}&\text{for } x \not= 1\\x+2&\text{for } x=2\end{cases}#