# How do you find the Vertical, Horizontal, and Oblique Asymptote given y = (x + 1)/(x - 1)?

Feb 7, 2017

The vertical asymptote is $x = 1$
The horizontal asymptote is $y = 1$
No oblique asymptote

#### Explanation:

As you cannot divide by $0$, $x \ne 1$

The vertical asymptote is $x = 1$

As the degree of the numerator $=$ the degree of the denominator, there is no oblique asymptote

${\lim}_{x \to + \infty} y = {\lim}_{x \to + \infty} \frac{x}{x} = 1$

The horizontal asymptote is $y = 1$

graph{(y-(x+1)/(x-1))(y-1)(y-100x+100)=0 [-8.1, 9.674, -4.8, 4.085]}