Confusing \(c\)

Algebra Level 5

\[y=\dfrac{x^2+2x+c}{x^2+4x+3c}\]

If the set of real values of \(c\) for which \(y\) can take all real values for \(x\in \mathbb{R}\) is in the form \((a,b)\), then find \(a+b\).