Answer
$-7$
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:
$$\lim_{x\to -1}\frac{f(x)-f(-1)}{x-(-1)}\\=\lim_{x\to -1}\frac{2x^2-3x-(2(-1)^2-3(-1))}{x+1}\\=\lim_{x\to -1}\frac{2x^2-3x-5}{x+1}\\=\lim_{x\to -1}\frac{(2x-5)(x+1)}{(x+1)}.$$
Cancel the common factors: $$\lim_{x\to -1}(2x-5)\\=2(-1)-5=-7$$
