State the excluded values of the given rational expression: \( \frac{x^{2}-5 x+3}{x^{2}-7 x+12} \)

To find the excluded values of the rational expression, we need to determine the values of \(x\) that make the denominator zero. The denominator is \(x^{2} - 7x + 12\). Factoring this polynomial gives us \((x - 3)(x - 4)\), which means the values that make the denominator zero are \(x = 3\) and \(x = 4\). Therefore, the excluded values are \(x = 3\) and \(x = 4\). Additionally, rational expressions cannot take on values that cause division by zero. This is why we have to set the denominator equal to zero and solve for \(x\). It’s a good reminder that excluded values often arise from simple quadratic factors!