Given that $f(x)=x^{2}-6 x$ and $g(x)=x+4$, find (a) $f+g=$ (b) $f-g=$ (c) $f g=$ (d) $f / g=$

Step 1 ：Given that $f(x)=x^{2}-6 x$ and $g(x)=x+4$

Step 2 ：For part (a), we need to add the functions $f(x)$ and $g(x)$. This means we add the corresponding terms of the functions. So, $f+g=x^{2}-6x+x+4=x^{2}-5x+4$

Step 3 ：For part (b), we need to subtract the function $g(x)$ from $f(x)$. This means we subtract the corresponding terms of $g(x)$ from $f(x)$. So, $f-g=x^{2}-6x-(x+4)=x^{2}-7x-4$

Step 4 ：For part (c), we need to multiply the functions $f(x)$ and $g(x)$. This means we multiply each term of $f(x)$ with each term of $g(x)$ and then add the results. So, $f g=(x^{2}-6x)(x+4)=x^{3}-2x^{2}-24x$

Step 5 ：For part (d), we need to divide the function $f(x)$ by $g(x)$. This means we divide each term of $f(x)$ by $g(x)$. So, $f / g=(x^{2}-6x)/(x+4)$

Step 6 ：Final Answer: (a) $f+g= \boxed{x^{2}-5x+4}$ (b) $f-g= \boxed{x^{2}-7x-4}$ (c) $f g= \boxed{x^{3}-2x^{2}-24x}$ (d) $f / g= \boxed{\frac{x^{2}-6x}{x+4}}$