Answer
$0$
Work Step by Step
Factor each polynomial:
$\lim _{x\rightarrow -1}\dfrac {\left( x+1\right) ^{2}}{x^{2}-1}
\\=\lim _{x\rightarrow -1}\dfrac {\left( x+1\right) ^{2}}{\left( x+1\right) \left( x-1\right) }$
Cancel the common factors:
$\\=\lim _{x\rightarrow -1}\dfrac {\left( x+1\right) }{\left( x-1\right) }
\\=\dfrac {-1+1}{-1-1}
\\=\dfrac{0}{-2}
\\=0$
