Question

tx math bridge - stage 2
rational expressions
progress:
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
identify the domain of the following rational expression: \\(\frac{x + 4}{x^2 + x - 12}\\)
\\(\circ\\) all real numbers except \\(-4\\) and \\(3\\).
\\(\circ\\) all real numbers except \\(4\\) and \\(-3\\).
\\(\circ\\) all real numbers except \\(-3\\).
\\(\circ\\) all real numbers except \\(3\\).

Explanation:

Step1: Factor denominator

$x^2 + x - 12 = (x + 4)(x - 3)$

Step2: Set denominator to zero

$(x + 4)(x - 3) = 0$

Step3: Solve for x

$x + 4 = 0 \Rightarrow x = -4$; $x - 3 = 0 \Rightarrow x = 3$

Step4: Determine domain

Exclude x=-4 and x=3 from real numbers.

Answer:

All real numbers except 3 and -4.