1. Problems states: Find the value of $x$ such that $$\frac{x^2 - 5x + 6}{x - 3} = 0.$$\n\n2. A fraction equals zero when its numerator equals zero and denominator is not zero. So, solve numerator $x^2 - 5x + 6 = 0$\n\n3. Factor numerator: $$x^2 - 5x + 6 = (x - 2)(x - 3).$$\n\n4. Set each factor equal to zero:\n\n\quad i. $x - 2 = 0 \implies x = 2$\n\quad ii. $x - 3 = 0 \implies x = 3$\n\n5. Check denominator $x-3 \neq 0$ to avoid division by zero. So $x \neq 3$.\n\n6. Therefore, the solution for the equation where the fraction equals zero is $$x = 2.$$