1. **State the problem:** Solve the equation $ (x - 1)(x + 1) = 4x - 5 $ for $ x $. 2. **Use the formula and expand:** The left side is a product of two binomials. Use the difference of squares formula: $$ (x - 1)(x + 1) = x^2 - 1^2 = x^2 - 1 $$ 3. **Rewrite the equation:** $$ x^2 - 1 = 4x - 5 $$ 4. **Bring all terms to one side to set the equation to zero:** $$ x^2 - 1 - 4x + 5 = 0 $$ 5. **Simplify:** $$ x^2 - 4x + 4 = 0 $$ 6. **Recognize the perfect square trinomial:** $$ (x - 2)^2 = 0 $$ 7. **Solve for $ x $:** $$ x - 2 = 0 \implies x = 2 $$ **Final answer:** $$ x = 2 $$