Answer
$\dfrac {7}{6}$
Work Step by Step
Factor each polynomial:
$\lim _{x\rightarrow -3}\dfrac {x^{2}-x-12}{x^{2}-9}
\\=\lim _{x\rightarrow -3}\dfrac {\left( x+3\right) \left( x-a\right) }{\left( x+3\right) \left( x-3\right) }$
Cancel the common factors:
$=\lim _{x\rightarrow -3}\dfrac {\left( x-4\right) }{\left( x-3\right) }
\\=\dfrac {-3-4}{-3-3}
\\=\dfrac {7}{6}$
