Given that $f(x)=x^{2}-5 x$ and $g(x)=x+14$, find
(a) $(f+g)(x)=$
(b) $(f-g)(x)=$
(c) $(f g)(x)=$
(d) $\left(\frac{f}{g}\right)(x)=$
Question Help: $\square$ Message instructor

Step 1 ：Given that $f(x)=x^{2}-5 x$ and $g(x)=x+14$, we need to find the sum, difference, product, and quotient of the functions $f(x)$ and $g(x)$.

Step 2 ：For (a), $(f+g)(x)$, we add the functions $f(x)$ and $g(x)$ together to get $x^{2} - 5x + x + 14 = x^{2} - 4x + 14$.

Step 3 ：For (b), $(f-g)(x)$, we subtract the function $g(x)$ from $f(x)$ to get $x^{2} - 5x - (x + 14) = x^{2} - 6x - 14$.

Step 4 ：For (c), $(fg)(x)$, we multiply the functions $f(x)$ and $g(x)$ together to get $(x^{2} - 5x)(x + 14) = x^{3} - 5x^{2} + 14x^{2} - 70x$.

Step 5 ：For (d), $\left(\frac{f}{g}\right)(x)$, we divide the function $f(x)$ by $g(x)$ to get $\frac{x^{2} - 5x}{x + 14}$.

Step 6 ：Final Answer: \[\boxed{(a)\ (f+g)(x) = x^{2} - 4x + 14,\ (b)\ (f-g)(x) = x^{2} - 6x - 14,\ (c)\ (fg)(x) = x^{3} - 5x^{2} + 14x^{2} - 70x,\ (d)\ \left(\frac{f}{g}\right)(x) = \frac{x^{2} - 5x}{x + 14}}\]