For what values of x is the expression \(\frac{3x-2}{4x^2+9x-9}\) undefined?
A
\(\frac{-3}{4} \hspace{1mm}or \hspace{1mm}3\)
B
\(\frac{-2}{3} \hspace{1mm}or \hspace{1mm}-3\)
C
\(\frac{2}{3} \hspace{1mm}or \hspace{1mm}3\)
D
\(\frac{3}{4} \hspace{1mm}or \hspace{1mm}-3\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
The equation \(\frac{3x - 2}{4x^2 + 9x - 9}\) is undefined when the denominator = 0.
\(4x^2 + 9x - 9 = 0\)
\(4x^2 + 12x - 3x - 9 = 0\)
\(4x(x + 3) - 3(x + 3) = 0\)
\((4x - 3)(x + 3) = 0\)
x = \(\frac{3}{4}\) or x = -3.
Source: Myschool Past Questions Archive (Record #26541)