Maxima

Calculus Level pending

If the maximum value in the \(4^\text{th} \) quadrant of the graph \(y = \dfrac{(x+5)(x+9)}{(x-5)(x-9)} \) is in the form \( - \dfrac{ \sqrt \alpha + \sqrt \beta}{\sqrt \alpha - \sqrt \beta} \), find \(\alpha + \beta\).

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