Recover a rational curve from points and a gradient

The equation of a curve $C$ is given by $y=ax+b+c/x$, where $a,b,c$ are constants. The gradient of $C$ at the point $(1,1)$ is 3. It is also given that $C$ passes through the point $(2,2)$. Find the values of $a,b,c$. Hence state the equations of the asymptotes of $C$.4 marks