We are asked to simplify the given rational expression: $\frac{x^2 - 5x + 6}{x - 3}$. This involves factoring the numerator and seeing if there are any common factors with the denominator that can be cancelled.

1. Problem Description

We are asked to simplify the given rational expression: $\frac{x^2 - 5x + 6}{x - 3}$. This involves factoring the numerator and seeing if there are any common factors with the denominator that can be cancelled.

2. Solution Steps

First, we factor the quadratic expression in the numerator, $x^2 - 5x + 6$. We are looking for two numbers that multiply to 6 and add to -

5. These numbers are -2 and -

3. So, the factored form of the numerator is $(x - 2)(x - 3)$.

Thus, we can rewrite the given expression as:

$\frac{(x - 2)(x - 3)}{x - 3}$

Now, we can cancel the common factor of $(x - 3)$ from the numerator and denominator, provided $x \ne 3$.

$\frac{(x - 2)(x - 3)}{x - 3} = x - 2$

3. Final Answer

$x - 2$