# How do you find any asymptotes of #f(x)=(x+3)/(x^2-4)#?

##### 1 Answer

There are two vertical asymptotes at

There is a horizontal asymptote at 0 as

There is a horizontal asymptote at 0 as

#### Explanation:

**Vertical Asymptotes**

These occur when the denominator is zero

**Horizontal Asymptotes**

We also need to examine the behaviour as

Now for large

We have,

and so, for large

so, as

and, as

**Summary**

There are two vertical asymptotes at

There is a horizontal asymptote at 0 as

There is a horizontal asymptote at 0 as

The graph validates this;

graph{(x+3)/((x+2)(x-2)) [-10, 10, -5, 5]}