Question 3 Find all values of the variable \( x \) for which the rational expression is undefined. \( \frac{8 x+19}{x^{2}+12 x+\frac{5}{5}} \) The expression is undefined when \( x=\square \) If there is more than one answer, write it as a list, using commas to senarato vour

To find where the rational expression \(\frac{8x+19}{x^{2}+12x+\frac{5}{5}}\) is undefined, we need to determine when the denominator is zero. First, simplify \(\frac{5}{5}\) to 1, giving us \(x^{2}+12x+1\). Thus, the expression is undefined when: \[ x^{2}+12x+1 = 0 \] To solve this quadratic equation, we could use the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\). Plugging in \(a=1\), \(b=12\), and \(c=1\): \[ x = \frac{-12 \pm \sqrt{12^2 - 4 \cdot 1 \cdot 1}}{2 \cdot 1} \] This simplifies to: \[ x = \frac{-12 \pm \sqrt{144 - 4}}{2} \] \[ x = \frac{-12 \pm \sqrt{140}}{2} \] This results in: \[ x = \frac{-12 \pm 2\sqrt{35}}{2} \] \[ x = -6 \pm \sqrt{35} \] Therefore, the values of \(x\) for which the expression is undefined are: \[ x = -6 + \sqrt{35}, -6 - \sqrt{35} \] So the expression is undefined when \(x = -6 + \sqrt{35}, -6 - \sqrt{35}\).