Question

multiple choice 8 points
where is the hole in the following rational function?
$f(x)=\frac{x^{2}-4}{x-2}$
$\bigcirc$ no hole
$\bigcirc$ $x=2$
$\bigcirc$ $x=4$
$\bigcirc$ $x=0$

Explanation:

Step1: Factor numerator

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

Step2: Find undefined x-value

Set denominator $x-2=0$, solve for $x$: $x=2$

Step3: Confirm common factor

$(x-2)$ is a common factor, so $x=2$ is a hole.

Answer:

$\boldsymbol{x=2}$ (matches the option marked as selected)