1. **Problem Statement:** Find the quotient function when dividing two functions, for example, given $f(x)$ and $g(x)$, find $\frac{f(x)}{g(x)}$. 2. **Formula:** The quotient of two functions $f(x)$ and $g(x)$ is given by: $$\frac{f(x)}{g(x)}$$ where $g(x) \neq 0$ to avoid division by zero. 3. **Important Rules:** - The domain of the quotient function excludes values where $g(x) = 0$. - Simplify the quotient by factoring numerator and denominator if possible. 4. **Example:** Suppose $f(x) = x^2 - 4$ and $g(x) = x - 2$. 5. **Step-by-step solution:** - Factor numerator: $x^2 - 4 = (x - 2)(x + 2)$. - Write quotient: $$\frac{f(x)}{g(x)} = \frac{(x - 2)(x + 2)}{x - 2}$$. - Simplify by canceling $x - 2$ (except where $x = 2$): $$x + 2$$. 6. **Domain:** All real numbers except $x = 2$ because $g(2) = 0$. 7. **Final answer:** $$\frac{f(x)}{g(x)} = x + 2, \quad x \neq 2$$. This quotient function behaves like $x + 2$ except at $x=2$ where it is undefined.