Answer
$\lim\limits_{x \to -2}\dfrac{3x^{2}+5x-2}{x+2}=-7$
Work Step by Step
$\lim\limits_{x \to -2}\dfrac{3x^{2}+5x-2}{x+2}$
Factor the numerator and simplify:
$\lim\limits_{x \to -2}\dfrac{3x^{2}+5x-2}{x+2}=\lim\limits_{x \to -2}\dfrac{(x+2)(3x-1)}{x+2}=\lim\limits_{x \to -2}3x-1$
Apply direct substitution to evaluate the limit:
$\lim\limits_{x \to -2}3x-1=3(-2)-1=-6-1=-7$
