For what values of x is the expression \(\frac{3x-2}{4x^2+9x-9}\) undefined?

For what values of x is the expression \(\frac{3x-2}{4x^2+9x-9}\) undefined?

Answer Details

The expression \(\frac{3x-2}{4x^2+9x-9}\) is undefined when the denominator is equal to zero. Therefore, we need to find the values of x that make the denominator zero. We can factor the denominator as follows: \[4x^2 + 9x - 9 = (4x - 3)(x + 3)\] So, the denominator is equal to zero when: \begin{align*} 4x - 3 &= 0 &\text{or} && x + 3 &= 0 \\ 4x &= 3 &&& x &= -3 \\ x &= \frac{3}{4} \end{align*} Therefore, the expression is undefined when \(x = \frac{3}{4}\) or \(x = -3\). So, the answer is \(\frac{3}{4} \hspace{1mm}or \hspace{1mm}-3\).