you are correct. the last factorization method is what i would use. don't worry that things don't look exactly the same algebraically. what we actually did was take 1/(x + 3) and multiply it by 1, namely by (x + 1)/(x + 1).

if you plot a graph of (x + 1)/(x^2 + 4x + 3), you would get exactly the same graph as the graph for 1/(x + 3)