Let $f(x) = x^2 + 3$ and $g(x) = x^2 + 8$. Find the following functions, and simplify each as much as possible: your final answer should be a polynomial with only one term in each power of $x$.

(a) $f(x) + g(x) =$

(b) $f(x) - g(x) =$

(c) $f(x) g(x) =$

(d) $\frac{f(x)}{g(x)} =$
(For part (d), you need not simplify as you did in (a)-(c).)