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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