<s>[INST] Find $x+y$, if integers $x$ and $y$ satisfy the equation $y+1/x=25/3$ Find $x+y$, if $x$ and $y$ are integers and satisfy the equation $y+1/x=25/3$
so I got to the answer by placing $3$ in the $x$ cause it looked like a fraction and $8$ was left for $y$, 
My question is: Is there any other/better way to solve this algebraically?
 [/INST] We have: $y = 8+\dfrac{x-3}{3x}\implies \dfrac{x-3}{3x}\in \mathbb{Z}\implies x-3=3nx\implies x-3nx=3\implies(3n-1)x=-3\implies x\mid 3 \implies x = \pm 1, \pm 3$. Since $y$ is an integer, $x = 3$. Thus $y = 8$, and $x+y = 3+8 = 11$.
</s>