Answer
$\dfrac {1}{2}$
Work Step by Step
Factor each polynomial:
$\lim _{x\rightarrow -1}\dfrac {x^{2}+x}{x^{2}-1}
\\=\lim _{x\rightarrow -1}\dfrac {x\left( x+1\right) }{\left( x-1\right) \left( x+1\right) }$
Cancel the common factors:
$=\lim _{x\rightarrow -1}\dfrac {x}{x-1}
\\=\dfrac {-1}{-1-1}
\\=\dfrac {-1}{-2}
\\=\dfrac {1}{2}
\\=0.5$
