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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 $a+b$ .

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by Akshat Sharda

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