1. **Problem statement:** ক. Express $$\frac{x^3 - 1}{x^3 + x^2 + x}$$ in factorized form. 2. **Formula and rules:** - Use difference of cubes: $$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$$. - Factor common terms in denominator. 3. **Step-by-step solution:** - Numerator: $$x^3 - 1 = (x - 1)(x^2 + x + 1)$$ (difference of cubes with $a=x$, $b=1$). - Denominator: $$x^3 + x^2 + x = x(x^2 + x + 1)$$ (factor out $x$). - Substitute back: $$\frac{x^3 - 1}{x^3 + x^2 + x} = \frac{(x - 1)(x^2 + x + 1)}{x(x^2 + x + 1)}$$ - Cancel common factor $x^2 + x + 1$: $$= \frac{x - 1}{x}$$ 4. **Final answer:** $$\boxed{\frac{x - 1}{x}}$$