Limits and Continuity

Given the function

$g(x)=\frac{x^2-5x+6}{x^2-4x+3}$

$($a$)$ Discuss whether $\underset{x{1}^{+}}{lim}g(x)$ and $\underset{x{1}^{-}}{lim}g(x)$ exist and are equal;

$($b$)$ Determine the points of discontinuity of $g.$