Tomamos como el límite
$$\lim_{x \to -1^+}\left(\frac{3 x^{2} + 1}{- x^{2} + \left(x + 2\right)}\right)$$
cambiamos
$$\lim_{x \to -1^+}\left(\frac{3 x^{2} + 1}{- x^{2} + \left(x + 2\right)}\right)$$
=
$$\lim_{x \to -1^+}\left(\frac{3 x^{2} + 1}{\left(-1\right) \left(x - 2\right) \left(x + 1\right)}\right)$$
=
$$\lim_{x \to -1^+}\left(- \frac{3 x^{2} + 1}{\left(x - 2\right) \left(x + 1\right)}\right) = $$
False
= oo
Entonces la respuesta definitiva es:
$$\lim_{x \to -1^+}\left(\frac{3 x^{2} + 1}{- x^{2} + \left(x + 2\right)}\right) = \infty$$