Simplify the following complex fractions: \( \begin{array}{ll}\text { (1) } \frac{2+\frac{1}{x}}{\frac{1}{x^{2}}} & \text { (2) } 3-\frac{x-\frac{9}{x}}{x-3}\end{array} \)

We need to simplify two complex fractions. Problem (1): Simplify (2 + 1/x) divided by (1/x²). Step 1. Write the expression as a single fraction:   (2 + 1/x) / (1/x²) Step 2. Multiply by the reciprocal of the denominator:   (2 + 1/x) × x² Step 3. Distribute x²:   2x² + (x² × (1/x)) = 2x² + x Thus, the simplified form is 2x² + x, or equivalently, x(2x + 1) (note that x ≠ 0). ──────────────────────────── Problem (2): Simplify 3 - [(x - (9/x))/(x - 3)]. Step 1. Rewrite the numerator x - (9/x) with a common denominator:   x - (9/x) = (x² - 9)/x Now the fraction becomes:   [(x² - 9)/x] ÷ (x - 3) = (x² - 9)/(x(x - 3)) Step 2. Notice that x² - 9 factors:   x² - 9 = (x - 3)(x + 3) So,   (x² - 9)/(x(x - 3)) = [(x - 3)(x + 3)]/(x(x - 3)) Step 3. Cancel the common factor (x - 3) (assuming x ≠ 3):   = (x + 3)/x Step 4. Now return to the full expression:   3 - [(x + 3)/x] Step 5. Combine over a common denominator x:   3 = 3x/x, so   3 - (x + 3)/x = (3x - (x + 3))/x = (3x - x - 3)/x = (2x - 3)/x Thus, the simplified form is (2x - 3)/x (with the restrictions x ≠ 0 and x ≠ 3). ──────────────────────────── Final Answers: 1) 2x² + x (or x(2x + 1)) 2) (2x - 3)/x