Question

question #4
determine the x - coordinate of the hole(s) of the following rational function: $y = \frac{5x^{2}+10x}{15x}$
$x = 15$
$x = 2$
$x = 0$
none

Explanation:

Step1: Factor the numerator

$5x^{2}+10x = 5x(x + 2)$

Step2: Simplify the rational - function

$y=\frac{5x(x + 2)}{15x}=\frac{x + 2}{3}$, $x
eq0$. The hole occurs at the value of $x$ that makes both the numerator and denominator of the original rational function equal to zero. The common factor between the numerator and denominator is $x$. Setting $x = 0$ makes both the numerator and denominator zero before simplification.

Answer:

C. $x = 0$