Is there a number $\displaystyle \alpha$ such that

$\displaystyle

\lim_{x \to -2}\frac{3x^2+\alpha x + \alpha + 3}{x^2 + x - 2}

$

exists? If so find the value of $\displaystyle \alpha$ and the value of the Limit

I tried first to factor the numerator into

$\displaystyle \left(x-1\right)\left(x+2\right)$

thinking this would reveal how to factor the numerator

to find $\displaystyle \alpha$ but nothing became obvious.

answer is $\displaystyle \alpha = 15$ limit $\displaystyle = -1$