Answer
Vertical asymptote: $x=1$
Horizontal asymptote: None
Work Step by Step
$t(x)=\dfrac{x^{2}+2}{x-1}$
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:
$x-1=0$
$x=1$
Horizontal asymptote:
The degree of the numerator is greater than the degree of the denominator. This function has no horizontal asymptote.