# How do you find vertical, horizontal and oblique asymptotes for y = (x^2+6x-7)/(x-1)?

Apr 6, 2017

There are no asymptotes.

#### Explanation:

The first step is to factorise the numerator and simplify.

$y = \frac{\left(x + 7\right) \cancel{\left(x - 1\right)}}{\cancel{\left(x - 1\right)}} = x + 7$

Since the factor (x - 1 ) has been removed this indicates there is a hole at x = 1

$y = x + 7 \text{ is the equation of a straight line }$ and has no asymptotes.

graph{(x^2+6x-7)/(x-1) [-32.47, 32.48, -16.23, 16.23]}