Find all numbers that must be excluded from the domain of the rational expression. (x-5)/(x^2)+7x+6 Type the values for which the rational expression is undefined. Select the correct choice below and fill in any answer boxes within your choice. A. I (Use a comma to separate answers as needed.) B. The rational expression is defined for all real

To find the numbers that must be excluded from the domain of the rational expression \(\frac{x-5}{x^{2}+7x+6}\), we need to determine when the denominator is equal to zero, as division by zero is undefined.<br /><br />The denominator is \(x^2 + 7x + 6\). We set this equal to zero and solve for \(x\):<br /><br />\[ x^2 + 7x + 6 = 0. \]<br /><br />This is a quadratic equation, which can be factored as:<br /><br />\[ (x + 1)(x + 6) = 0. \]<br /><br />Setting each factor equal to zero gives us the solutions:<br /><br />1. \(x + 1 = 0 \Rightarrow x = -1\),<br />2. \(x + 6 = 0 \Rightarrow x = -6\).<br /><br />Therefore, the values \(x = -1\) and \(x = -6\) must be excluded from the domain because they make the denominator zero.<br /><br />The correct choice is:<br />A. \(-1, -6\)