1. **State the problem:** Simplify the expression $$\frac{c^2 d^2 - 2 c d x + x^2}{c d - x}$$. 2. **Recognize the numerator:** The numerator is a perfect square trinomial. It can be factored using the formula $$a^2 - 2ab + b^2 = (a - b)^2$$ where $$a = c d$$ and $$b = x$$. 3. **Factor the numerator:** $$ c^2 d^2 - 2 c d x + x^2 = (c d - x)^2 $$ 4. **Rewrite the expression:** $$ \frac{(c d - x)^2}{c d - x} $$ 5. **Simplify by canceling common factors:** $$ \frac{\cancel{(c d - x)} (c d - x)}{\cancel{c d - x}} = c d - x $$ 6. **Final answer:** $$ c d - x $$ This simplification works as long as $$c d - x \neq 0$$ to avoid division by zero.