1. Distribute the Negative Sign!
$\frac{A}{C} - \frac{B + D}{C} = \frac{A - (B + D)}{C} = \frac{A - B - D}{C}$
2. Unlike Denominators (LCD)
$\frac{A}{B} - \frac{C}{D} = \frac{AD - BC}{BD}$
3. Opposite Denominators
$\frac{A}{b - a} = -\frac{A}{a - b} \implies \frac{X}{a - b} - \frac{A}{b - a} = \frac{X + A}{a - b}$
4. Always Factor to Simplify
$\frac{x^2 - 25}{x - 5} = \frac{(x - 5)(x + 5)}{x - 5} = x + 5$