For what values of x is the expression \(\frac{3x-2}{4x^2+9x-9}\) undefined?
Question 1 Report
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 \(\frac{3}{4} \hspace{1mm}or \hspace{1mm}-3\).
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