# Split This Maximization Into Two Parts

Algebra Level 5

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 $$a+b.$$

×