Question

find the domain of the rational function,
$f(x) = \frac{4(x + 2)(x + 3)}{(x + 5)(x - 5)}$.
\bigcirc a. $(-\infty, -5) \cup (5, \infty)$
\bigcirc b. $(-\infty, 5) \cup (5, \infty)$
\bigcirc c. $(-\infty, -5) \cup (-5, 5) \cup (5, \infty)$
\bigcirc d. $(-\infty, -3) \cup (-3, -2) \cup (-2, \infty)$

Explanation:

Step1: Identify denominator zero points

Set denominator equal to 0: $(x+5)(x-5)=0$
Solve: $x+5=0 \implies x=-5$; $x-5=0 \implies x=5$

Step2: Exclude zero points from domain

Rational function is defined for all real numbers except $x=-5$ and $x=5$.

Answer:

C. $(-\infty,-5)\cup(-5,5)\cup(5,\infty)$