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Let $a,b,c$ be three integers greater than $0$, and assume there is a real number $t$ such that $$ \frac{a}{a+b}=\frac{\left\lfloor t\right\rfloor}{\left\lfloor t\right\rfloor+1}. $$ Is there a way to show that $c$ is bounded in the interval $[a-d,a+d]$ for some $d$ constant, if we would say that $\frac{t}{t+1}=\frac{c}{c+b}$? Is there other stuff needed to be verifies first?

Thanks.

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