Answer:
x = −1, 1
Step-by-step explanation:
Vertical Asymptotes
A vertical asymptote of the graph of a given function f(x) is the line x=a, such that one of of these statements is fulfilled
[tex]\displaystyle \lim _{x\to a^{+}}f(x)=\pm \infty[/tex]
[tex]\displaystyle \lim _{x\to a^{+}}f(x)=\pm \infty[/tex]
If f(x) is a rational expression, we must find all the values of x who make the denominator equal to zero
[tex]\displaystyle f(x)=\frac{2x^2+3x+6}{x^2-1}[/tex]
We set the denominator to zero
[tex]x^2-1=0[/tex]
[tex](x-1)(x+1)=0[/tex]
[tex]x=-1,\ x=1[/tex]
Those are the vertical asymptotes of f
