Question

x+1 over x divided by x-2 over x; options: factor, improper fraction, complex fraction

Explanation:

Step1: Analyze each term

• For \(\frac{x + 1}{x}\): It is a rational expression, not an improper fraction (improper fraction is for integers in numerator/denominator) or a complex fraction yet.
• For \(\frac{\frac{x + 1}{x}}{\frac{x - 2}{x}}\): A complex fraction is a fraction where the numerator, denominator, or both are fractions. Here, the numerator is \(\frac{x + 1}{x}\) and the denominator is \(\frac{x - 2}{x}\), so this is a complex fraction.
• "factor" is about breaking down expressions, not matching here. "improper fraction" is for fractions with integer numerator/denominator where numerator ≥ denominator, not applicable here.

Answer:

The term \(\frac{\frac{x + 1}{x}}{\frac{x - 2}{x}}\) matches with "complex fraction".