Why do we use factoring to simplify rational expressions

The video tutorial covers simplifying fractions and polynomials. It begins with a review of simplifying the fraction 12/8 by finding the greatest common factor, resulting in 3/2. The tutorial then transitions to factoring polynomials, using the example of X^2 - 4X + 3 divided by X - 3. The instructor explains the process of factoring and simplifying expressions by identifying common factors, drawing parallels between numerical and polynomial simplification.

Explain how you can divide out common factors in the expression (X^2 - 4X + 3) / (X - 3).

Can the expression X^2 - 4X + 3 be factored? If so, what are the factors?