# How do you find the asymptotes for #y = (x-2)/( x^2-4)#?

##### 2 Answers

Vertical asymptote at

#### Explanation:

First, we can simplify the expression.

#(x-2)/(x^2-4)=(x-2)/((x+2)(x-2))=1/(x+2)#

Here, the

Our new function is

**Vertical asymptotes:**

The vertical asymptotes will occur when the denominator of the function equals

#x+2=0#

#x=-2#

There is a vertical asymptote at

**Horizontal asymptotes:**

When the degree of the denominator is greater than the denominator of the numerator, the

We can check a graph:

graph{(x-2)/(x^2-4) [-10, 10, -5, 5]}

The asymptote is

#### Explanation:

This is how I got that asymptote.

First, I factored everything as much as I can. It's like taking apart a puzzle to see every piece of it.

Now,

So now the equation looks like this:

So let's find the value that makes

We can always check our work by graphing

graph{(x-2)/((x+2) (x-2))}