1. **Problem:** Simplify the expression $$\frac{x^2 - 4x}{x - 2} \cdot \frac{2 - x}{x}$$ and describe any restrictions on the variables. 2. **Step 1: Factor expressions where possible.** - Factor numerator of first fraction: $$x^2 - 4x = x(x - 4)$$ - Note that $$2 - x = -(x - 2)$$ 3. **Rewrite the expression using these factors:** $$\frac{x(x - 4)}{x - 2} \cdot \frac{-(x - 2)}{x}$$ 4. **Step 2: Multiply the fractions:** $$\frac{x(x - 4)}{x - 2} \times \frac{-(x - 2)}{x} = \frac{x(x - 4) \cdot -(x - 2)}{(x - 2) \cdot x}$$ 5. **Step 3: Cancel common factors:** $$\frac{\cancel{x}(x - 4) \cdot -\cancel{(x - 2)}}{\cancel{(x - 2)} \cdot \cancel{x}} = -(x - 4)$$ 6. **Step 4: Simplify the expression:** $$-(x - 4) = -x + 4$$ 7. **Step 5: State restrictions:** - Denominators cannot be zero. - From $$x - 2 \neq 0$$, so $$x \neq 2$$. - From $$x \neq 0$$ (denominator in second fraction). **Final answer:** $$-x + 4$$ with restrictions $$x \neq 0, 2$$.