ANSWER
The limit is -4
EXPLANATION
[tex] \displaystyle\lim_{x\to -2} \dfrac{x^2-4}{x+2} [/tex]
The numerator factors into (x-2)(x+2)
[tex] \displaystyle\lim_{x\to -2} \dfrac{(x-2)(x+2)}{x+2} [/tex]
The (x+2) cancel out
[tex] \displaystyle\lim_{x\to -2} (x-2) [/tex]
By direct substitution
[tex] \displaystyle\lim_{x\to -2} (x-2) = -2 -2 = -4 [/tex]
[tex] \displaystyle
\lim_{x\to -2}\dfrac{x^2-4}{x+2}=
\lim_{x\to -2}\dfrac{(x-2)(x+2)}{x+2}=
\lim_{x\to -2}(x-2)=-2-2=-4 [/tex]
