To simplify the given expression by reducing it to a single fraction, follow these steps:
1. Find a common denominator for the two fractions. The denominators are (x-2)(x-1) and 3.
2. Rewrite the fractions with the common denominator.
3. Combine the fractions into a single fraction.
Here is the simplified expression in a single fraction:
\[ \frac{2x - 3}{3} \div \frac{x-2}{x-1} = \frac{(2x - 3)(x-1)}{3(x-2)} \]
So, the simplified expression is:
\[ \frac{2x^2 - 2x - 3x + 3}{3x - 6} = \frac{2x^2 - 5x + 3}{3x - 6} \]
