An algebra problem by Anirudha Brahma

Algebra Level 5

\[ \dfrac{a+3c}{a+2b+c} + \dfrac{4b}{a+b+2c} - \dfrac{8c}{a+b+3c} \]

Let \(a,b\) and \(c\) be positive reals. If the minimum value of the expression above can be expressed as \(x + y\sqrt 2\), where \(x\) and \(y\) are integers, find \(x+y\).

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