# Min Factor

Algebra Level 4

Define $y=\dfrac{x^2+2x+3}{x^2-2x+3}$

for real number $$x$$.

If the minimum value of $$y$$ can be expressed as $$a+b\sqrt c$$ where $$a$$, $$b$$, $$c$$ are integers and $$c$$ is not a perfect square, then find the value of $$\dfrac {a+b+c}{2}$$.

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