1. Let's create an equation where all terms cancel out at the end. 2. Consider the equation $$\frac{x^2 - 1}{x - 1} = x + 1$$. 3. The numerator can be factored using the difference of squares: $$x^2 - 1 = (x - 1)(x + 1)$$. 4. Substitute the factorization into the equation: $$\frac{(x - 1)(x + 1)}{x - 1} = x + 1$$. 5. We can cancel the common factor $x - 1$ in numerator and denominator: $$\frac{\cancel{(x - 1)}(x + 1)}{\cancel{(x - 1)}} = x + 1$$. 6. After cancellation, the equation simplifies to $$x + 1 = x + 1$$. 7. This means the equation holds true for all values of $x$ except $x = 1$ where the original denominator is zero. 8. So, the equation is designed such that everything cancels out, leaving an identity. Final answer: $$\frac{x^2 - 1}{x - 1} = x + 1$$ where all terms cancel except the restriction $x \neq 1$.