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\frac{\sqrt{7}(\sqrt{7} + \sqrt{3})}{(\sqrt{7} - \sqrt{3})(\sqrt{7} + \sqrt{3})} = \frac{7 + \sqrt{21}}{7 - 3} = \frac{7 + \sqrt{21}}{4}
The rationalized form is $ \boxed{\dfrac{7 + \sqrt{21}}{4}} $.
Question: The functions $ f(x) = x^2 - 6x + m $ and $ g(x) = x^2 - 6x + 3m $ are evaluated at $ x = 5 $. If $ f(5) = 2g(5) $, find $ m $.

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