Answer
$0$
Work Step by Step
General formula for average rate of change from $a$ to $b$: $\frac{f(b)-f(a)}{b-a}.$
Factor each polynomial:
$$\lim_{x\to -1}\frac{f(x)-f(-1)}{x-(-1)}\\=\lim_{x\to -1}\frac{x^2+2x-((-1)^2+2(-1))}{x+1}\\=\lim_{x\to -1}\frac{x^2+2x+1}{x+1}\\=\lim_{x\to -1}\frac{(x+1)(x+1)}{(x+1)}.$$
Cancel the common factors: $$\lim_{x\to -1}(x+1)\\=(-1)+1=0$$
