Is there a general relation between $a/b$ and $(a+c)/(b+c)$ where $a,b,c > 0 $? Is there a general relation between $a/b$ and $(a+c)/(b+c)$ where $a,b> 0$ and $c\geq 0$ ? 
Is there a general proof for that relation ? 

$\frac{a+c}{b+c}$ is between $\frac ab$ and $\frac cc=1$, hence whether $\frac{a+c}{b+c}>\frac ab$ or $\frac{a+c}{b+c}<\frac ab$ (or $\frac{a+c}{b+c}=\frac ab$) depends on how $\frac ab$ compares to $1$, i.e. how $a$ compares to $b$.
