Question

1. identify the restrictions on the variable.

\\(\frac{x^2 + 3x + 2}{x^2 - 4x - 12}\\)
options:
\\(x \
eq -2\\)
\\(x \
eq 0\\)
\\(x \
eq -2\\) and \\(x \
eq 6\\)
\\(x \
eq -1\\) and \\(x \
eq -2\\)

Explanation:

Step1: Set denominator equal to zero

$x^2 - 4x - 12 = 0$

Step2: Factor the quadratic equation

$(x - 6)(x + 2) = 0$

Step3: Solve for x

$x - 6 = 0 \Rightarrow x = 6$; $x + 2 = 0 \Rightarrow x = -2$

Step4: Determine restrictions

$x
eq -2$ and $x
eq 6$

Answer:

X ≠ -2 and X ≠ 6