Answer
$\dfrac {5}{4}$
Work Step by Step
Factor each polynomial:
$\lim _{x\rightarrow -3}\dfrac {x^{2}+x-6}{x^{2}+2x-3}
\\=\lim _{x\rightarrow -3}\dfrac {\left( x+3\right) \left( x-2\right) }{\left( x+3\right) \left( x-1\right) }$
Cancel the common factors:
$\\=\lim _{x\rightarrow -3}\dfrac {\left( x-2\right) }{\left( x-1\right) }
\\=\dfrac {-3-2}{-3-1}
\\=\dfrac {-5}{-4}
\\=\dfrac {5}{4}$
