# Determine the value of "a" so that the following limit exists? Lim (3x^2+ax+a+3)/x^2+x+2 x->-2

$\frac{3 {x}^{2} + a x + a + 3}{{x}^{2} + x + 2} x \to - 2$
not only does the limit exist, but it even works without the use of a limit as the denominator does not become 0 when you put$x = - 2$ but instead becomes $4$ so we're not dividing by 0 and therefore have no need of even using a limit