Confusing cc

Algebra Level 5

y=x2+2x+cx2+4x+3cy=\dfrac{x^2+2x+c}{x^2+4x+3c}

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

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