Let $f(x)=\frac{1}{x-4}$ and $g(x)=5x+11$.
Then $(f\circ g)(3)=◻$,
$$(f\circ g)(x)=◻\text{. }$$

Step 1 ：Given the functions $f(x)=\frac{1}{x-4}$ and $g(x)=5x+11$, we are asked to find the composition of these functions, denoted as $(f\circ g)(x)$ and $(f\circ g)(3)$.

Step 2 ：The notation $(f\circ g)(x)$ means $f(g(x))$.

Step 3 ：First, let's find $(f\circ g)(3)$.

Step 4 ：We know that $g(3)=5\ast 3+11=26$.

Step 5 ：So, $(f\circ g)(3)=f(g(3))=f(26)$.

Step 6 ：We know that $f(x)=\frac{1}{x-4}$, so $f(26)=\frac{1}{26-4}=\frac{1}{22}$.

Step 7 ：$\boxed{{\displaystyle (f\circ g)(3)=\frac{1}{22}}}$.

Step 8 ：Next, let's find $(f\circ g)(x)$.

Step 9 ：We know that $g(x)=5x+11$, so $(f\circ g)(x)=f(g(x))=f(5x+11)$.

Step 10 ：We know that $f(x)=\frac{1}{x-4}$, so $f(5x+11)=\frac{1}{5x+11-4}=\frac{1}{5x+7}$.

Step 11 ：$\boxed{{\displaystyle (f\circ g)(x)=\frac{1}{5x+7}}}$.