The function $g$ is defined by $g(x)=\frac{-3+2 x}{4+x}$. Find $g(x+4)$ \[ g(x+4)= \]

Step 1 ：The function $g(x)$ is given by $g(x)=\frac{-3+2 x}{4+x}$.

Step 2 ：To find $g(x+4)$, we replace $x$ with $x+4$ in the function.

Step 3 ：This gives us $g(x+4)=\frac{-3+2 (x+4)}{4+(x+4)}$.

Step 4 ：The simplified expression for $g(x+4)$ is $\frac{2x+5}{x+8}$.

Step 5 ：Final Answer: $g(x+4)=\boxed{\frac{2x+5}{x+8}}$