Answer
$-1$
Work Step by Step
Recall:
(1) $\lim _{x\rightarrow c}\dfrac {f\left( x\right) }{g\left( x\right) }=\dfrac {\lim _{x\rightarrow c}f\left( x\right) }{\lim _{x\rightarrow c}g\left( x\right) }$
(2) $\lim _{x\rightarrow c}f(x) = f(c)$
Use the rules above to have:
$\lim _{x\rightarrow 0}\dfrac {x^{2}-4}{x^{2}+4}
\\=\dfrac {\lim _{x\rightarrow 0}\left( x^{2}-4\right) }{\lim _{x\rightarrow 0}\left( x^{2}+4\right) }
\\=\dfrac {0-4}{0+4}
\\=-1$
