Simplifying Strategy

1. Factor the numerator completely
2. Factor the denominator completely
3. Cancel common factors

Important: You can only cancel factors, not terms!

Restrictions

Values that make the denominator zero are excluded from the domain.

Example: $\frac{x + 3}{x - 5}$

Restriction: $x \neq 5$ (denominator would be zero)

Common Mistakes to Avoid

❌ Wrong: $\frac{x + 3}{x} = 3$ (can't cancel terms!)

✓ Correct: $\frac{x + 3}{x}$ cannot be simplified further

Step 2: Factor the denominator (perfect square trinomial) $x^2 + 6x + 9 = (x + 3)^2 = (x + 3)(x + 3)$

Step 3: Write and cancel $\frac{(x + 3)(x - 3)}{(x + 3)(x + 3)} = \frac{x - 3}{x + 3}$

Restriction: $x \neq -3$

Answer: $\frac{x - 3}{x + 3}$ (where $x \neq -3$)

Step 2: Factor denominator (difference of squares) $x^2 - 4 = (x + 2)(x - 2)$

Step 3: Write and cancel $(x - 2)$ $\frac{(x - 2)(x^2 + 2x + 4)}{(x + 2)(x - 2)} = \frac{x^2 + 2x + 4}{x + 2}$

Restrictions: $x \neq 2, -2$

Answer: $\frac{x^2 + 2x + 4}{x + 2}$ (where $x \neq \pm 2$)