# 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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