Question: Simplify.
2 - \frac{3}{x} - \frac{1}{x^2}
(Assume all nonzero denominators.)
= \square
1. **State the problem:** Simplify the expression $$2 - \frac{3}{x} - \frac{1}{x^2}$$ assuming all denominators are nonzero.
2. **Find a common denominator:** The denominators are $$1$$, $$x$$, and $$x^2$$. The least common denominator (LCD) is $$x^2$$.
3. **Rewrite each term with the LCD:**
$$2 = \frac{2x^2}{x^2}$$
$$- \frac{3}{x} = - \frac{3x}{x^2}$$
$$- \frac{1}{x^2} = - \frac{1}{x^2}$$
4. **Combine all terms over the common denominator:**
$$\frac{2x^2}{x^2} - \frac{3x}{x^2} - \frac{1}{x^2} = \frac{2x^2 - 3x - 1}{x^2}$$
5. **Factor the numerator if possible:**
Factor $$2x^2 - 3x - 1$$:
$$2x^2 - 3x - 1 = (2x + 1)(x - 1)$$
6. **Write the simplified expression:**
$$\frac{(2x + 1)(x - 1)}{x^2}$$
**Final answer:**
$$\boxed{\frac{(2x + 1)(x - 1)}{x^2}}$$