Finding the Constant c for a Limit Problem

[Kuma]

limits problem solving help!

Alrighty so i have no idea where to even start...

Find the constant c such that

Lim
x-> 3

x^2+x+c
-----------
X^2 - 5x + 6


exists

Yeah so

so far i got as far as factoring the bottom

(x-3)(x-2)

And now i have no idea where to go from there
any ideas?

 

[Pere Callahan]

As x-->3, the denominator tends to zero, so for the limit to have the slightest chance to exist, the numerator must approach zero as well. For which value of c does it do so?

 

[lurflurf]

require
(x-3)|(x^2+x+c)
that is find and "a" such that
(x-3)(x+a)=(x^2+x+c)
then set c=-3a