$2.(2-3$ pts$)$ Evaluate the following limit:

$\underset{x-3}{lim}\frac{x^2+4x+3}{(x+3)|x+1|}$

$($a$)$ The limit does not exist

$($b$)-1$

$($c$)1$

$($d$)2$

$($e$)-2$

$(x+3)(x+1)$