question find all vertical asymptotes of the following function. f(x) = (3x + 15)/(x^2 + 10x + 9) answer no…

Explanation:

Step1: Factor the denominator

Factor $x^{2}+10x + 9$ as $(x + 1)(x+9)$. So $f(x)=\frac{3x + 15}{(x + 1)(x + 9)}$.

Step2: Find values that make denominator 0

Set the denominator equal to 0: $(x + 1)(x + 9)=0$. Using the zero - product property, if $ab = 0$, then $a=0$ or $b = 0$. So $x+1=0$ gives $x=-1$ and $x + 9=0$ gives $x=-9$.

Answer:

$x=-1,x=-9$