Final answer:
The fraction (2x-3) / (3x-3) cannot be further simplified as there are no common factors that can be canceled out. We would keep the fraction as it is after ensuring there isn't an opportunity for simplification through factoring or other algebraic methods.
Step-by-step explanation:
The question asks for the simplified form of the complex fraction (2x-3) / (3x-3). To simplify this, we first note that the expressions in the numerator and denominator do not have common factors, except for 1, and thus cannot be directly simplified by canceling out the same quantities. However, we can look for other algebraic manipulations. In this case, since no obvious simplification can be made, we would keep the fraction as it is, ensuring we have accounted for the possibility of factoring, which is not applicable here.
To perform simplifications of fractions in general, we multiply numerators and multiply denominators, simplifying by common factors as needed. If we had a common factor, it would be the same quantity in the numerator and the denominator, and any fraction with the same quantity in both would equal 1. Since that is not the case here, the fraction remains (2x-3) / (3x-3).
If we were given an expression such as x² / x², where the numerator and denominator are the same, then we could say that the fraction equals 1 because any number divided by itself is 1. This holds true for any variable or expression as long as the expressions are identical and the denominator is not equal to zero.