Which of the following is a value of \( x \) for which the expression \( \frac{-3}{x^{2}+3 x-12} \) is undefined?

To find the value of \( x \) for which the expression \( \frac{-3}{x^{2}+3x-12} \) is undefined, we need to determine when the denominator of the expression is equal to zero. The denominator of the expression is \( x^{2}+3x-12 \). To find the values of \( x \) for which the denominator is zero, we need to solve the equation \( x^{2}+3x-12 = 0 \). Let's solve the equation \( x^{2}+3x-12 = 0 \) to find the values of \( x \) for which the expression is undefined. Solve the quadratic equation by following steps: - step0: Solve using the quadratic formula: \(x^{2}+3x-12=0\) - step1: Solve using the quadratic formula: \(x=\frac{-3\pm \sqrt{3^{2}-4\left(-12\right)}}{2}\) - step2: Simplify the expression: \(x=\frac{-3\pm \sqrt{57}}{2}\) - step3: Separate into possible cases: \(\begin{align}&x=\frac{-3+\sqrt{57}}{2}\\&x=\frac{-3-\sqrt{57}}{2}\end{align}\) - step4: Rewrite the fraction: \(\begin{align}&x=\frac{-3+\sqrt{57}}{2}\\&x=-\frac{3+\sqrt{57}}{2}\end{align}\) - step5: Rewrite: \(x_{1}=-\frac{3+\sqrt{57}}{2},x_{2}=\frac{-3+\sqrt{57}}{2}\) The values of \( x \) for which the expression \( \frac{-3}{x^{2}+3x-12} \) is undefined are \( x = -\frac{3+\sqrt{57}}{2} \) and \( x = \frac{-3+\sqrt{57}}{2} \).