Answer
$\frac{3}{2}$
Work Step by Step
Factor each polynomial:
$$\lim_{x\to -2^+}\frac{x^2+x-2}{x^2+2x}\\=\lim_{x\to -2^+}\frac{(x+2)(x-1)}{(x)(x+2)}.$$
Cancel the common factors: $$\lim_{x\to -2^+}\frac{(x-1)}{(x)}\\=\frac{-2-1}{-2}=\frac{3}{2}$$