1. Like Denominators
$\frac{A}{C} + \frac{B}{C} = \frac{A + B}{C}$
2. Unlike Denominators (LCD)
$\frac{A}{B} + \frac{C}{D} = \frac{AD + BC}{BD}$
3. Opposite Denominators
$\frac{A}{b - a} = -\frac{A}{a - b}$
4. Always Factor to Simplify
$\frac{x + 3}{x^2 - 9} = \frac{x + 3}{(x - 3)(x + 3)} = \frac{1}{x - 3}$