Find $y''$ in terms of $x$ and $y$ when when $xy=3x+8y$.

Question

The question is in the title (could not post it here for some reason). Came up with an answer $(y-3)/(x-8)^2$, but I am not sure if I have done it right.

Answer 1

$$xy=3x+8y$$

$$y+xy'=3+8y',y'=\frac{3-y}{x-8}$$ $$2y'+xy''=8y'',y''=\frac{-2y'}{x-8}=\frac{-2\frac{3-y}{x-8}}{x-8}=\frac{2(y-3)}{(x-8)^2}$$