Split This Maximization Into Two Parts

Algebra Level 4

For real numbers \(x\) and \(y,\) the maximum possible value for

\[5-y^2-4y-x^2+xy+3x\]

can be expressed as \(\frac{a}{b}\) where \(a\) and \(b\) are positive coprime integers. Find \(a+b.\)

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