Let $f(x) = 2 x^2 - 6 x + 5$ and $g(x)= x^2 + 4.$ Find $f+g$, $f-g$, $f \cdot g$, and $\displaystyle \frac{f}{g}$. Simplify your answers.

---

1. $f+g =$

2. $f-g =$

3. $f \cdot g =$

4. $\displaystyle \frac{f}{g} =$

---