limits, finding value of b

Quote:

Is there a number b such that $\displaystyle \lim_{x \to -1} \frac{2x^2+bx+3b}{x^2-x-2}$ exists? If so, find the value of b and the value of the limit.

I'm just going to plug -1 into the denominator and that gives 0.

$\displaystyle -1^2-(-1)-2=0$

So for the numerator I am going to plug in -1 as well and solve for b

$\displaystyle 2(-1)^2+b(-1)+3b=0$

That gives me $\displaystyle b=-1$

And $\displaystyle \lim_{x \to -1} \frac{2x^2-x-3}{x^2-x-2}=\frac{5}{3}$

Am I doing it right? Thanks