Answer
Vertical asymptotes: $x=1$ and $x=-1$
Horizontal asymptote: $y=0$
Work Step by Step
$r(x)=\dfrac{2x-3}{x^{2}-1}$
Vertical asymptote
A rational function has vertical asymptotes where the function is undefined, that is, where the denominator is zero.
Set the denominator equal to $0$ and solve for $x$ to find the vertical asymptotes of this function:
$x^{2}-1=0$
$x^{2}=1$
$\sqrt{x^{2}}=\sqrt{1}$
$x=\pm1$
Horizontal asymptote
Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is $y=0$