Question

what is the value of the rational expression \\(\frac{x^2 - 2x - 3}{4x^2 - 12}\\) when \\(x = 3\\)? options: \\(-\frac{1}{4}\\), \\(0\\), \\(\frac{1}{4}\\), undefined

Explanation:

Step1: Substitute $x=3$ into numerator

$$\begin{align*} x^2 - 2x - 3 &= 3^2 - 2(3) - 3 \\ &= 9 - 6 - 3 \\ &= 0 \end{align*}$$

Step2: Substitute $x=3$ into denominator

$$\begin{align*} 4x^2 - 12 &= 4(3)^2 - 12 \\ &= 4(9) - 12 \\ &= 36 - 12 \\ &= 24 \end{align*}$$

Step3: Evaluate the rational expression

$\frac{0}{24} = 0$

Answer:

0